Fix missing import in finiterectlat-scatter.py

Stupid typo with possibly serious consequences...

.drone.yml

@@ -0,0 +1,83 @@
+---
+kind: pipeline
+type: docker
+name: buildqpms-alpine-preinstlibs
+
+workspace:
+  path: /home/qpmsbuild/qpms
+
+# don't run in master until the python/lapacke linking problem is resolved
+trigger:
+  branch:
+    exclude: 
+      - master
+
+steps:
+- name: chown
+  image: qpms/buildenv/alpine/pkgdnumlib
+  pull: never
+  commands:
+    - chown -R qpmsbuild.qpmsbuild .
+- name: submodules
+  image: qpms/buildenv/alpine/pkgdnumlib
+  pull: never
+  user: qpmsbuild
+  commands:
+    - git submodule init
+    - git submodule update
+- name: build
+  image: qpms/buildenv/alpine/pkgdnumlib
+  pull: never
+  user: qpmsbuild
+  commands:
+  - cmake -DCMAKE_INSTALL_PREFIX=$HOME/.local .
+  - make install
+  - export LIBRARY_PATH=$HOME/.local/lib
+  - python3 setup.py install --user
+  - cd examples/rectangular/modes
+  - pip3 install --user matplotlib #needed to run the example
+  - export LD_LIBRARY_PATH=$HOME/.local/lib
+  - ./01a_realfreq_svd.sh
+
+---
+kind: pipeline
+type: docker
+name: buildqpms-debian-preinstlibs
+
+workspace:
+  path: /home/qpmsbuild/qpms
+
+steps:
+- name: chown
+  image: qpms/buildenv/debian/pkgdnumlib
+  pull: never
+  commands:
+    - chown -R qpmsbuild.qpmsbuild .
+- name: submodules
+  image: qpms/buildenv/debian/pkgdnumlib
+  pull: never
+  user: qpmsbuild
+  commands:
+    - git submodule init
+    - git submodule update
+- name: build
+  image: qpms/buildenv/debian/pkgdnumlib
+  pull: never
+  user: qpmsbuild
+  commands:
+  - cmake -DCMAKE_INSTALL_PREFIX=/home/qpmsbuild/.local .
+  - make install
+  - export LIBRARY_PATH=$HOME/.local/lib
+  - python3 setup.py install --user
+  - pip3 install --user matplotlib #needed to run the examples
+  - export LD_LIBRARY_PATH=$HOME/.local/lib
+  - cd examples/rectangular/modes
+  - ./01a_realfreq_svd.sh
+  - cd -
+  - cd examples/hexagonal/modes
+  #- ./01a_realfreq_svd.sh 
+  #- ./01_compute_modes.sh 
+  #- ./02b_compute_disp_0M.sh 
+  #- ./02_compute_disp.sh 
+  #- ./02x_compute_disp.sh
+

.gitignore

@@ -5,4 +5,29 @@
 *.pdf
 *.o
 docs/*
+
 qpms/qpms_c.c
+qpms/cy*.c
+CMakeCache.txt
+CMakeFiles/*
+faddeeva/*
+qpms/CMakeFiles/*
+qpms/libqpms.so
+qpms/cmake_install.cmake
+qpms_version.c
+qpms.egg_info/*
+dist/*
+build/*
+Makefile
+CTestTestfile.cmake
+
+amos/CMakeFiles/*
+amos/Makefile
+amos/amos_mangling.h
+cmake_install.cmake
+cython_debug/*
+qpms.egg-info/*
+tests/CmakeFiles/*
+tests/cmake_install.cmake
+tests/CMakeFiles/*
+

.gitmodules

@@ -0,0 +1,4 @@
+[submodule "camos"]
+	path = camos
+	url = https://codeberg.org/QPMS/zbessel.git
+	branch = purec

CLIUTILS.md

@@ -0,0 +1,43 @@
+Overview of QPMS command line utilities
+=======================================
+
+The utilities are located in the `misc` directory. Run the
+utility with `-h` argument to get more info.
+
+
+Rectangular and square 2D lattices
+----------------------------------
+
+These scripts deal with simple 2D rectangular lattices,
+finite or infinite, one scatterer per unit cell. 
+\f$ D_{2h} \f$ or \f$ D_{4h} \f$ symmetric adapted bases
+are used where applicable.
+
+### Finite lattices
+
+ * `finiterectlat-modes.py`:  Search for resonances using Beyn's algorithm.
+ * `finiterectlat-scatter.py`:  Plane wave scattering.
+ * `finiterectlat-constant-driving.py`: Rectangular array response to
+   a driving where a subset of particles are excited by basis VSWFs with the
+   same phase.
+
+### Infinite lattices
+
+ * `rectlat_simple_modes.py`: Search for lattice modes using Beyn's algorithm.
+ * `infiniterectlat-k0realfreqsvd.py`: 
+    Evaluate the lattice mode problem singular values at the Γ point for a real frequency interval.
+    Useful as a starting point in lattice mode search before using Beyn's algorithm.
+ * `infiniterectlat-scatter.py`: Plane wave scattering.
+
+
+General 2D lattices
+-------------------
+
+### Infinite lattices
+
+These can contain several scatterers per unit cell. Symmetry adapted bases currently not implemented.
+
+ * `lat2d_modes.py`: Search for lattice modes using Beyn's algorithm.
+ * `lat2d_realfreqsvd.py`: 
+    Evaluate the lattice mode problem singular values at the Γ point for a real frequency interval.
+    Useful as a starting point in lattice mode search before using Beyn's algorithm.

CMakeLists.txt

@@ -1,10 +1,16 @@
 cmake_minimum_required(VERSION 3.0.2)
+
+option(QPMS_USE_FORTRAN_AMOS "Use the original AMOS Fortran libraries instead of the C ones" OFF)
+
+if (QPMS_USE_FORTRAN_AMOS)
 include(CMakeAddFortranSubdirectory)
+endif (QPMS_USE_FORTRAN_AMOS)
 include(version.cmake)
+include(GNUInstallDirs)
 
 project (QPMS)
 
-set(CMAKE_BUILD_TYPE Debug)
+list(APPEND CMAKE_MODULE_PATH "${CMAKE_CURRENT_SOURCE_DIR}/cmake/")
 
 macro(use_c99)
   if (CMAKE_VERSION VERSION_LESS "3.1")
@@ -23,9 +29,27 @@ set(CMAKE_POSITION_INDEPENDENT_CODE ON)
 
 set (QPMS_VERSION_MAJOR 0)
 #set (QPMS_VERSION_MINOR 3)
-cmake_add_fortran_subdirectory (amos
-	PROJECT amos
-	LIBRARIES amos
-	NO_EXTERNAL_INSTALL)
+
+if (QPMS_USE_FORTRAN_AMOS)
+	cmake_add_fortran_subdirectory (amos
+		PROJECT amos
+		LIBRARIES amos
+		NO_EXTERNAL_INSTALL)
+	set(QPMS_AMOSLIB amos)
+else (QPMS_USE_FORTRAN_AMOS)
+	set(CAMOS_BUILD_STATIC ON)
+	add_subdirectory (camos)
+	set(QPMS_AMOSLIB camos)
+endif (QPMS_USE_FORTRAN_AMOS)
+
+
+set(FADDEEVA_BUILD_STATIC ON)
+add_subdirectory(faddeeva)
+
 add_subdirectory (qpms)
+
+
+enable_testing()
+add_subdirectory (tests EXCLUDE_FROM_ALL)
+
 #add_subdirectory (apps/transop-ewald)

COPYING.md

@@ -0,0 +1,675 @@
+### GNU GENERAL PUBLIC LICENSE
+
+Version 3, 29 June 2007
+
+Copyright (C) 2007 Free Software Foundation, Inc.
+<https://fsf.org/>
+
+Everyone is permitted to copy and distribute verbatim copies of this
+license document, but changing it is not allowed.
+
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+
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+software and other kinds of works.
+
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+#### 11. Patents.
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+A patent license is "discriminatory" if it does not include within the
+scope of its coverage, prohibits the exercise of, or is conditioned on
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+license was granted, prior to 28 March 2007.
+
+Nothing in this License shall be construed as excluding or limiting
+any implied license or other defenses to infringement that may
+otherwise be available to you under applicable patent law.
+
+#### 12. No Surrender of Others' Freedom.
+
+If conditions are imposed on you (whether by court order, agreement or
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+excuse you from the conditions of this License. If you cannot convey a
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+consequence you may not convey it at all. For example, if you agree to
+terms that obligate you to collect a royalty for further conveying
+from those to whom you convey the Program, the only way you could
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+from conveying the Program.
+
+#### 13. Use with the GNU Affero General Public License.
+
+Notwithstanding any other provision of this License, you have
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+
+#### 14. Revised Versions of this License.
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+The Free Software Foundation may publish revised and/or new versions
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+will be similar in spirit to the present version, but may differ in
+detail to address new problems or concerns.
+
+Each version is given a distinguishing version number. If the Program
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+
+If the Program specifies that a proxy can decide which future versions
+of the GNU General Public License can be used, that proxy's public
+statement of acceptance of a version permanently authorizes you to
+choose that version for the Program.
+
+Later license versions may give you additional or different
+permissions. However, no additional obligations are imposed on any
+author or copyright holder as a result of your choosing to follow a
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+
+#### 15. Disclaimer of Warranty.
+
+THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY
+APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT
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+#### 16. Limitation of Liability.
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+TO OPERATE WITH ANY OTHER PROGRAMS), EVEN IF SUCH HOLDER OR OTHER
+PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES.
+
+#### 17. Interpretation of Sections 15 and 16.
+
+If the disclaimer of warranty and limitation of liability provided
+above cannot be given local legal effect according to their terms,
+reviewing courts shall apply local law that most closely approximates
+an absolute waiver of all civil liability in connection with the
+Program, unless a warranty or assumption of liability accompanies a
+copy of the Program in return for a fee.
+
+END OF TERMS AND CONDITIONS
+
+### How to Apply These Terms to Your New Programs
+
+If you develop a new program, and you want it to be of the greatest
+possible use to the public, the best way to achieve this is to make it
+free software which everyone can redistribute and change under these
+terms.
+
+To do so, attach the following notices to the program. It is safest to
+attach them to the start of each source file to most effectively state
+the exclusion of warranty; and each file should have at least the
+"copyright" line and a pointer to where the full notice is found.
+
+        <one line to give the program's name and a brief idea of what it does.>
+        Copyright (C) <year>  <name of author>
+
+        This program is free software: you can redistribute it and/or modify
+        it under the terms of the GNU General Public License as published by
+        the Free Software Foundation, either version 3 of the License, or
+        (at your option) any later version.
+
+        This program is distributed in the hope that it will be useful,
+        but WITHOUT ANY WARRANTY; without even the implied warranty of
+        MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+        GNU General Public License for more details.
+
+        You should have received a copy of the GNU General Public License
+        along with this program.  If not, see <https://www.gnu.org/licenses/>.
+
+Also add information on how to contact you by electronic and paper
+mail.
+
+If the program does terminal interaction, make it output a short
+notice like this when it starts in an interactive mode:
+
+        <program>  Copyright (C) <year>  <name of author>
+        This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
+        This is free software, and you are welcome to redistribute it
+        under certain conditions; type `show c' for details.
+
+The hypothetical commands \`show w' and \`show c' should show the
+appropriate parts of the General Public License. Of course, your
+program's commands might be different; for a GUI interface, you would
+use an "about box".
+
+You should also get your employer (if you work as a programmer) or
+school, if any, to sign a "copyright disclaimer" for the program, if
+necessary. For more information on this, and how to apply and follow
+the GNU GPL, see <https://www.gnu.org/licenses/>.
+
+The GNU General Public License does not permit incorporating your
+program into proprietary programs. If your program is a subroutine
+library, you may consider it more useful to permit linking proprietary
+applications with the library. If this is what you want to do, use the
+GNU Lesser General Public License instead of this License. But first,
+please read <https://www.gnu.org/licenses/why-not-lgpl.html>.

Doxyfile

@@ -51,7 +51,7 @@ PROJECT_BRIEF          = "Electromagnetic multiple scattering library and toolki
 # and the maximum width should not exceed 200 pixels. Doxygen will copy the logo
 # to the output directory.
 
-PROJECT_LOGO           =
+PROJECT_LOGO           = farfield.png
 
 # The OUTPUT_DIRECTORY tag is used to specify the (relative or absolute) path
 # into which the generated documentation will be written. If a relative path is
@@ -753,7 +753,7 @@ WARN_LOGFILE           =
 # spaces.
 # Note: If this tag is empty the current directory is searched.
 
-INPUT                  = qpms notes finite_systems.md README.md README.Triton.md finite_systems.md lattices.md TODO.md
+INPUT                  = qpms notes misc finite_systems.md MIRRORS.md CLIUTILS.md README.md README.Triton.md finite_systems.md lattices.md TODO.md
 
 # This tag can be used to specify the character encoding of the source files
 # that doxygen parses. Internally doxygen uses the UTF-8 encoding. Doxygen uses
@@ -773,7 +773,7 @@ INPUT_ENCODING         = UTF-8
 # *.md, *.mm, *.dox, *.py, *.f90, *.f, *.for, *.tcl, *.vhd, *.vhdl, *.ucf,
 # *.qsf, *.as and *.js.
 
-FILE_PATTERNS          =
+FILE_PATTERNS          = 
 
 # The RECURSIVE tag can be used to specify whether or not subdirectories should
 # be searched for input files as well.
@@ -1462,7 +1462,7 @@ MATHJAX_FORMAT         = HTML-CSS
 # The default value is: http://cdn.mathjax.org/mathjax/latest.
 # This tag requires that the tag USE_MATHJAX is set to YES.
 
-MATHJAX_RELPATH        = http://cdn.mathjax.org/mathjax/latest
+MATHJAX_RELPATH        = https://uslugi.necada.org/js/mathjax
 
 # The MATHJAX_EXTENSIONS tag can be used to specify one or more MathJax
 # extension names that should be enabled during MathJax rendering. For example

MIRRORS.md

@@ -0,0 +1,14 @@
+QPMS source code mirrors
+========================
+
+QPMS source code is available at several locations; in all of the following,
+upstream `master` branch is kept up-to-date. Various development branches
+are not necessarily pushed everywhere (and they should be considered
+unstable in the sense that rebases and forced pushes are possible).
+
+mirror                                          | note                    | provider                                          | backend
+----------------------------------------------- | ----------------------- | ------------------------------------------------- | ------
+<https://repo.or.cz/qpms.git>                   | primary public upstream | [repo.or.cz](https://repo.or.cz/)                 | girocco
+<https://codeberg.org/QPMS/qpms>                |                         | [Codeberg](https://codeberg.org)                  | gitea
+<https://git.piraattipuolue.fi/QPMS/qpms.git>   |                         | [Pirate Party Finland](https://piraattipuolue.fi) | gitea
+<https://version.aalto.fi/gitlab/qpms/qpms.git> |                         | [Aalto University](https://aalto.fi)              | gitlab 

README.md

@@ -1,10 +1,14 @@
+[![Build Status](https://drone.perkele.eu/api/badges/QPMS/qpms/status.svg)](https://drone.perkele.eu/QPMS/qpms)
+
 QPMS README
 ===========
 
-QPMS is a toolkit for frequency-domain simulations of photonic systems
+[QPMS][homepage] (standing for QPMS Photonic Multiple Scattering) 
+is a toolkit for frequency-domain simulations of photonic systems
 consisting of compact objects (particles) inside a homogeneous medium. Scattering
 properties of the individual particles are described by their T-matrices
-(which can be obtained e.g. with the `scuff-tmatrix` tool from 
+(which can be obtained using one of the built-in generators or
+ e.g. with the `scuff-tmatrix` tool from 
 the [SCUFF-EM] suite).
 
 QPMS handles the multiple scattering of electromagnetic radiation between 
@@ -12,26 +16,39 @@ the particles. The system can consist either of a finite number of particles
 or an infinite number of periodically arranged lattices (with finite number
 of particles in a single unit cell).
 
+
 Features
 ========
 
+
 Finite systems
 --------------
- * Computing multipole excitations *and fields (TODO)* scattered from nanoparticle
+ * Computing multipole excitations and fields scattered from nanoparticle
    clusters illuminated by plane, spherical or *cylindrical (TODO)* waves.
- * Finding eigenmodes.
- * *Calculating cross sections (TODO).*
+ * Finding eigenmodes (optical resonances).
+ * Calculating cross sections.
  * Reducing numerical complexity of the computations by exploiting
    symmetries of the cluster (decomposition to irreducible representations).
 
+
 Infinite systems (lattices)
 ---------------------------
- * 2D-periodic systems supported. (TODO 1D and 3D.)
- * *Calculation of transmission and reflection properties (TODO).*
+ * 2D-periodic systems with arbitrary unit cell geometry supported. (TODO 1D and 3D.)
+ * Computing multipole excitations and fields scattered from nanoparticle
  * Finding eigenmodes and calculating dispersion relations.
- * *Calculation of far-field radiation patterns of an excited array (TODO).*
- * Reducing numerical complexity of the computations by exploiting
-   symmetries of the lattice (decomposition to irreducible representations).
+ * Calculation of the scattered fields.
+ * *Calculation of total transmission and reflection properties (TODO).*
+ * *Reducing numerical complexity of the computations by exploiting
+   symmetries of the lattice (decomposition to irreducible representations) (in development).* 
+
+
+Getting the code
+================
+
+The codebase is available at the main upstream public repository
+<https://repo.or.cz/qpms.git> or any of the [maintained mirrors][MIRRORS].
+Just clone the repository with `git` and proceed to the installation instructions
+below.
 
 
 Installation
@@ -47,30 +64,49 @@ you can [get the source and compile it yourself][GSL].
 
 You also need a fresh enough version of [cmake][].
 
-After GSL is installed, you can install qpms to your local python library using::
+QPMS uses a C version of the Amos library for calculating Bessel function
+from a submodule. Before proceeding with running `cmake`, the submodules
+need to be downloaded first (in the QPMS source root directory):
 
 ```{.sh}
-  cmake .
-  make amos
-  python3 setup.py install --user
+  git submodule init
+  git submodule update
 ```
 
-If GSL is not installed the standard library path on your system, you might 
-need to pass it to the installation script using the
-`LIBRARY_PATH` and `LD_LIBRARY_PATH` environment
-variables.
+After GSL is installed and submodules updated, you can install qpms to your local python library using
 
-Special care has often be taken when installing QPMS in cluster environments.
+```{.sh}
+  cmake -DCMAKE_INSTALL_PREFIX=${YOUR_PREFIX} .
+  make install
+  python3 setup.py install --user
+```
+Above, replace `${YOUR_PREFIX}` with the path to where you want to install the shared library;
+you will also need to make sure that the linker can find it;
+on Linux, this means the path `${YOUR_PREFIX}/lib` is included in your
+`LIBRARY_PATH` and `LD_LIBRARY_PATH` environment variables. The same applies
+to the GSL and OpenBLAS dependencies: they must be installed where the
+installation scripts and linker can find them (setting the `C_INCLUDE_PATH` environment
+variable might be necessary as well).
+
+Special care might need to be taken when installing QPMS in cluster environments.
 Specific installation instructions for Aalto University's Triton cluster
 can be found in a [separate document][TRITON-README].
 
+Instructions for installation on Android-based devices are
+in [another document][INSTALL-ANDROID].
+
+
 Documentation
 =============
 
-Documentation of QPMS is a work in progress. Most of the newer code
-is documented using [doxygen][] comments. To build the documentation, just run
+[QPMS documentation][homepage] is a work in progress. Most of the newer code
+is documented using [doxygen][] comments. Documentation generated for the
+upstream version is hosted on the QPMS homepage <https://qpms.necada.org>.
+
+To build the documentation yourself, 
+just run
 `doxygen`
-in the root directory; the documentation will then be found in 
+in the QPMS source root directory; the documentation will then be found in 
 `docs/html/index.html`.
 
 Of course, the prerequisite of this is having doxygen installed.
@@ -82,14 +118,77 @@ under root.
 Tutorials
 ---------
 
-  * [Infinite system (lattice) tutorial][tutorial-infinite]
   * [Finite system tutorial][tutorial-finite]
 
+See also the examples directory in the source repository.
+
+
+Command line utilities
+----------------------
+
+  * [Overview of the Python command line utilities][cliutils]
+
+
+Acknowledgments
+================
+
+This software has been developed in the [Quantum Dynamics research group][QD],
+Aalto University, Finland. If you use the code in your work, please cite 
+**M. Nečada and P. Törmä, Multiple-scattering T-matrix simulations for nanophotonics: symmetries and periodic lattices, [arXiv: 2006.12968][lepaper] (2020)**
+in your publications, presentations, and similar. 
+
+Please also have a look at other publications by the group 
+(google scholar Päivi Törmä), they may be useful for your work as well. 
+
+
+Bug reports
+===========
+
+If you believe that some parts of QPMS behave incorrectly, please mail
+a bug report to [marek@necada.org][authormail]. To ensure that your message is not
+considered spam, please start the subject line with `QPMS`.
+
+If you were able to fix a bug yourself, please include the patch as well,
+see below.
+
+
+Contributions
+=============
+
+Contributions to QPMS are welcome, be it bug fixes, improvements to the
+documentation, code quality, or new features.
+
+You can send patches prepared using the 
+[`git format-patch`](https://git-scm.com/docs/git-format-patch) tool
+to [marek@necada.org][authormail].
+
+If you plan to contribute with major changes to the codebase, it is 
+recommended to discuss that first (see the contact information below).
+
+
+Contact & discussion
+====================
+
+You can contact the main author e.g. via [e-mail][authormail]
+or [Telegram](https://t.me/necadam).
+
+You are also warmly welcome to the [QPMS user chat][telegramchat]
+in Telegram!
+
+
+[homepage]: https://qpms.necada.org
 [SCUFF-EM]: https://homerreid.github.io/scuff-em-documentation/
 [OpenBLAS]: https://www.openblas.net/
 [GSL]: https://www.gnu.org/software/gsl/
 [cmake]: https://cmake.org
 [TRITON-README]: README.Triton.md
+[INSTALL-ANDROID]: notes/INSTALL_ANDROID.md
 [tutorial-finite]: finite_systems.md
 [tutorial-infinite]: lattices.md
 [doxygen]: http://doxygen.nl/
+[QD]: https://www.aalto.fi/en/department-of-applied-physics/quantum-dynamics-qd
+[lepaper]: https://arxiv.org/abs/2006.12968
+[telegramchat]: https://t.me/QPMScattering
+[authormail]: mailto:marek@necada.org
+[cliutils]: CLIUTILS.md
+[MIRRORS]: MIRRORS.md

TODO.md

@@ -1,11 +1,12 @@
-TODO list before public release
-===============================
+TODO list before 1.0 release
+============================
 
 - Tests!
 - Docs!
-- Cross section calculations.
-- Field calculations.
-- Complex frequencies, n's, k's.
+- Cross section calculations. (Done in some Python scripts.)
+- Field calculations. (Partly done, needs more testing.)
+  * Also test periodic vs. nonperiodic consistence (big finite lattice + absorbing medium vs. infinite lattice + absorbing medium).
+- Complex frequencies, n's, k's. (Mostly done.)
 - Transforming point (meta)generators.
 - Check whether moble's quaternions and my 
   quaternions give the same results in tmatrices.py
@@ -24,8 +25,12 @@ TODO list before public release
   * As a description of a T-matrix / particle metadata.
 - Nice CLI for all general enough utilities.
 - Remove legacy code.
-- Split qpms_c.pyx.
+- Split `qpms_c.pyx`.
 - Reduce compiler warnings.
+- Serialisation (saving, loading) of `ScatteringSystem` and other structures.
+- Python exceptions instead of hard crashes in the C library where possible.
+- Scatsystem init sometimes fail due to rounding errors and hardcoded absolute tolerance 
+  in the `qpms_tmatrix_isclose()` call.
 - Prefix all identifiers. Maybe think about a different prefix than qpms?
 - Consistent indentation and style overall.
 - Rewrite the parallelized translation matrix, mode problem matrix generators
@@ -36,3 +41,16 @@ Nice but less important features
 
 - Static, thread-safe caches of constant coefficients + API without the current "calculators".
 
+
+Optimisations
+-------------
+
+- Leaving out the irrelevant elements if a "rectangular" block of the translations matrix is needed.
+- Ewald sums with "non-parallel" shifts (are about 20 times slower than the purely parallel ones).
+- Reusing intermediate results (profiling needed)
+  * Bessel, Legendre functions (see also branch `finite_lattice_speedup`)
+  * Lattice points (sorting and scaling)
+  * Γ/Δ functions (for periodic lattices)
+- More parallelisation.
+- Possibly pre-calculation of the (precise) coefficients in Bessel and Legendre functions (using gmp)
+- Asymptotic approximations of the Bessel functions for far fields.

amos/camos.h

@@ -0,0 +1,30 @@
+#ifndef CAMOS_H_
+#define CAMOS_H_
+#include "amos.h"
+
+// TODO what about all the INTEGER_t and DOUBLE_PRECISION_t?
+
+static inline int camos_zbesh(double zr, double zi, double fnu, int kode, int m,
+          int n, double *cyr, double *cyi, int *nz) {
+	int ierr;
+	amos_zbesh(&zr, &zi, &fnu, &kode, &m, &n, cyr, cyi, nz, &ierr);
+	return ierr;
+}
+
+static inline int camos_zbesj(double zr, double zi, double fnu, int kode, int n, double *cyr,
+          double *cyi, int *nz) {
+	int ierr;
+	double cwrkr[n], cwrki[n];
+	amos_zbesj(&zr, &zi, &fnu, &kode, &n, cyr, cyi, nz, &ierr);
+	return ierr;
+}
+
+static inline int camos_zbesy(double zr, double zi, double fnu, int kode, int n, double *cyr,
+          double *cyi, int *nz, double *cwrkr, double *cwrki) {
+	int ierr;
+	amos_zbesy(&zr, &zi, &fnu, &kode, &n, cyr, cyi, nz, cwrkr, cwrki, &ierr);
+	return ierr;
+}
+
+
+#endif // CAMOS_H_

besseltransforms/2-1-3

@@ -0,0 +1,2 @@
+((k^2*(-3 + Sqrt[1 + k^2/(c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2)/Sqrt[1 + k^2/(c - I*k0)^2] - (2*(k^2*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2))/Sqrt[1 + k^2/(2*c - I*k0)^2] + (k^2*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2)/Sqrt[1 + k^2/(3*c - I*k0)^2])/(k^3*k0)
+SeriesData[k, Infinity, {(8*c^2)/(k*k0), (-15*(2*c^3 - I*c^2*k0))/(k*k0), 0, (35*(18*c^5 - (25*I)*c^4*k0 - 12*c^3*k0^2 + (2*I)*c^2*k0^3))/(4*k*k0), 0, (63*(-138*c^7 + (301*I)*c^6*k0 + 270*c^5*k0^2 - (125*I)*c^4*k0^3 - 30*c^3*k0^4 + (3*I)*c^2*k0^5))/(8*k*k0), 0, (165*(3110*c^9 - (9075*I)*c^8*k0 - 11592*c^7*k0^2 + (8428*I)*c^6*k0^3 + 3780*c^5*k0^4 - (1050*I)*c^4*k0^5 - 168*c^3*k0^6 + (12*I)*c^2*k0^7))/(64*k*k0)}, 2, 11, 1]

besseltransforms/2-1-4

@@ -0,0 +1,2 @@
+((k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4)/(Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) - (2*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4))/(Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) + (k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4)/(Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)))/(k^4*k0)
+SeriesData[k, Infinity, {(15*c^2)/(k*k0), (-48*(2*c^3 - I*c^2*k0))/(k*k0), (35*(25*c^4 - (24*I)*c^3*k0 - 6*c^2*k0^2))/(4*k*k0), 0, (-21*(301*c^6 - (540*I)*c^5*k0 - 375*c^4*k0^2 + (120*I)*c^3*k0^3 + 15*c^2*k0^4))/(8*k*k0), 0, (-99*(-3025*c^8 + (7728*I)*c^7*k0 + 8428*c^6*k0^2 - (5040*I)*c^5*k0^3 - 1750*c^4*k0^4 + (336*I)*c^3*k0^5 + 28*c^2*k0^6))/(64*k*k0), 0, (-143*(28501*c^10 - (93300*I)*c^9*k0 - 136125*c^8*k0^2 + (115920*I)*c^7*k0^3 + 63210*c^6*k0^4 - (22680*I)*c^5*k0^5 - 5250*c^4*k0^6 + (720*I)*c^3*k0^7 + 45*c^2*k0^8))/(128*k*k0)}, 2, 11, 1]

besseltransforms/2-1-5

@@ -0,0 +1,2 @@
+((k^4*(-5 + Sqrt[1 + k^2/(c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4)/Sqrt[1 + k^2/(c - I*k0)^2] - (2*(k^4*(-5 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4))/Sqrt[1 + k^2/(2*c - I*k0)^2] + (k^4*(-5 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4)/Sqrt[1 + k^2/(3*c - I*k0)^2])/(k^5*k0)
+SeriesData[k, Infinity, {(24*c^2)/(k*k0), (-105*(2*c^3 - I*c^2*k0))/(k*k0), (32*(25*c^4 - (24*I)*c^3*k0 - 6*c^2*k0^2))/(k*k0), (-315*(18*c^5 - (25*I)*c^4*k0 - 12*c^3*k0^2 + (2*I)*c^2*k0^3))/(4*k*k0), 0, (231*(138*c^7 - (301*I)*c^6*k0 - 270*c^5*k0^2 + (125*I)*c^4*k0^3 + 30*c^3*k0^4 - (3*I)*c^2*k0^5))/(8*k*k0), 0, (429*(-3110*c^9 + (9075*I)*c^8*k0 + 11592*c^7*k0^2 - (8428*I)*c^6*k0^3 - 3780*c^5*k0^4 + (1050*I)*c^4*k0^5 + 168*c^3*k0^6 - (12*I)*c^2*k0^7))/(64*k*k0)}, 2, 11, 1]

besseltransforms/2-1-6

@@ -0,0 +1,2 @@
+((k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) - (2*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6))/(Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) + (k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6)/(Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)))/(k^6*k0)
+SeriesData[k, Infinity, {(35*c^2)/(k*k0), (-192*(2*c^3 - I*c^2*k0))/(k*k0), (315*(25*c^4 - (24*I)*c^3*k0 - 6*c^2*k0^2))/(4*k*k0), (-320*(18*c^5 - (25*I)*c^4*k0 - 12*c^3*k0^2 + (2*I)*c^2*k0^3))/(k*k0), (231*(301*c^6 - (540*I)*c^5*k0 - 375*c^4*k0^2 + (120*I)*c^3*k0^3 + 15*c^2*k0^4))/(8*k*k0), 0, (429*(-3025*c^8 + (7728*I)*c^7*k0 + 8428*c^6*k0^2 - (5040*I)*c^5*k0^3 - 1750*c^4*k0^4 + (336*I)*c^3*k0^5 + 28*c^2*k0^6))/(64*k*k0), 0, (429*(28501*c^10 - (93300*I)*c^9*k0 - 136125*c^8*k0^2 + (115920*I)*c^7*k0^3 + 63210*c^6*k0^4 - (22680*I)*c^5*k0^5 - 5250*c^4*k0^6 + (720*I)*c^3*k0^7 + 45*c^2*k0^8))/(128*k*k0)}, 2, 11, 1]

besseltransforms/2-1-7

@@ -0,0 +1,2 @@
+((k^6*(-7 + Sqrt[1 + k^2/(c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/Sqrt[1 + k^2/(c - I*k0)^2] - (2*(k^6*(-7 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6))/Sqrt[1 + k^2/(2*c - I*k0)^2] + (k^6*(-7 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6)/Sqrt[1 + k^2/(3*c - I*k0)^2])/(k^7*k0)
+SeriesData[k, Infinity, {(48*c^2)/(k*k0), (-315*(2*c^3 - I*c^2*k0))/(k*k0), (160*(25*c^4 - (24*I)*c^3*k0 - 6*c^2*k0^2))/(k*k0), (-3465*(18*c^5 - (25*I)*c^4*k0 - 12*c^3*k0^2 + (2*I)*c^2*k0^3))/(4*k*k0), (128*(301*c^6 - (540*I)*c^5*k0 - 375*c^4*k0^2 + (120*I)*c^3*k0^3 + 15*c^2*k0^4))/(k*k0), (3003*(-138*c^7 + (301*I)*c^6*k0 + 270*c^5*k0^2 - (125*I)*c^4*k0^3 - 30*c^3*k0^4 + (3*I)*c^2*k0^5))/(8*k*k0), 0, (2145*(3110*c^9 - (9075*I)*c^8*k0 - 11592*c^7*k0^2 + (8428*I)*c^6*k0^3 + 3780*c^5*k0^4 - (1050*I)*c^4*k0^5 - 168*c^3*k0^6 + (12*I)*c^2*k0^7))/(64*k*k0)}, 2, 11, 1]

besseltransforms/2-2-1

@@ -0,0 +1,2 @@
+((-2*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0))/k + ((-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0))/k + (Sqrt[Pi]*(Piecewise[{{0, k^2/k0^2 <= 1}}, (2*Sqrt[k^2 - k0^2])/(k*Sqrt[Pi])] + I*Piecewise[{{(2*k0)/(k*Sqrt[Pi]), k0^2/k^2 < 1}, {(2*(k0 - Sqrt[-k^2 + k0^2]))/(k*Sqrt[Pi]), k0^2/k^2 > 1}}, 0]))/2)/k0^2
+Piecewise[{{SeriesData[k, Infinity, {c^2/k0^2, 0, (3*c^2)/2 - (7*c^4)/(4*k0^2) + ((3*I)*c^3)/k0, 0, (31*c^6 - (90*I)*c^5*k0 - 105*c^4*k0^2 + (60*I)*c^3*k0^3 + 15*c^2*k0^4)/(8*k0^2), 0, (-5*(127*c^8 - (504*I)*c^7*k0 - 868*c^6*k0^2 + (840*I)*c^5*k0^3 + 490*c^4*k0^4 - (168*I)*c^3*k0^5 - 28*c^2*k0^6))/(64*k0^2), 0, (7*(511*c^10 - (2550*I)*c^9*k0 - 5715*c^8*k0^2 + (7560*I)*c^7*k0^3 + 6510*c^6*k0^4 - (3780*I)*c^5*k0^5 - 1470*c^4*k0^6 + (360*I)*c^3*k0^7 + 45*c^2*k0^8))/(128*k0^2)}, 2, 11, 1], (k0 <= 0 && k^2/k0^2 > 1) || k0 > 0}}, SeriesData[k, Infinity, {-k0^(-2), 0, (2*c^2 + k0^2)/(2*k0^2), 0, ((c*(c - I*k0)^3)/4 - (c*(2*c - I*k0)^3)/4 - I/4*(c - I*k0)^3*k0 + I/8*(2*c - I*k0)^3*k0)/k0^2, 0, (-(c*(c - I*k0)^5)/8 + (c*(2*c - I*k0)^5)/8 + I/8*(c - I*k0)^5*k0 - I/16*(2*c - I*k0)^5*k0)/k0^2, 0, ((5*c*(c - I*k0)^7)/64 - (5*c*(2*c - I*k0)^7)/64 - (5*I)/64*(c - I*k0)^7*k0 + (5*I)/128*(2*c - I*k0)^7*k0)/k0^2, 0, ((-7*c*(c - I*k0)^9)/128 + (7*c*(2*c - I*k0)^9)/128 + (7*I)/128*(c - I*k0)^9*k0 - (7*I)/256*(2*c - I*k0)^9*k0)/k0^2}, 0, 11, 1]]

besseltransforms/2-2-2

@@ -0,0 +1,2 @@
+(-1 + (4*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2)/k^2 - (2*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2)/k^2 + Sqrt[Pi]*(I*Piecewise[{{0, k^2/k0^2 <= 1}}, (2*k0*Sqrt[k^2 - k0^2])/(k^2*Sqrt[Pi])] + Piecewise[{{(k^2 + 2*k0*(-k0 + Sqrt[-k^2 + k0^2]))/(k^2*Sqrt[Pi]), k^2/k0^2 < 1}, {(1 - (2*k0^2)/k^2)/Sqrt[Pi], k^2/k0^2 > 1}}, 0]))/(2*k0^2)
+SeriesData[k, Infinity, {(2*c^2)/k0^2, (-3*(c^3 - I*c^2*k0))/k0^2, 0, (5*(3*c^5 - (7*I)*c^4*k0 - 6*c^3*k0^2 + (2*I)*c^2*k0^3))/(4*k0^2), 0, (-7*(9*c^7 - (31*I)*c^6*k0 - 45*c^5*k0^2 + (35*I)*c^4*k0^3 + 15*c^3*k0^4 - (3*I)*c^2*k0^5))/(8*k0^2), 0, (15*(85*c^9 - (381*I)*c^8*k0 - 756*c^7*k0^2 + (868*I)*c^6*k0^3 + 630*c^5*k0^4 - (294*I)*c^4*k0^5 - 84*c^3*k0^6 + (12*I)*c^2*k0^7))/(64*k0^2)}, 2, 11, 1]

besseltransforms/2-2-3

@@ -0,0 +1,2 @@
+(k^2*(-3 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 - 2*k^2*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) - 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + k^2*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3)/(3*k^3*k0^2)
+SeriesData[k, Infinity, {(3*c^2)/k0^2, (-16*c^3)/k0^2 + ((8*I)*c^2)/k0, (-15*c^2)/2 + (125*c^4)/(4*k0^2) - ((30*I)*c^3)/k0, 0, (-7*(301*c^6 - (540*I)*c^5*k0 - 375*c^4*k0^2 + (120*I)*c^3*k0^3 + 15*c^2*k0^4))/(24*k0^2), 0, (9*(3025*c^8 - (7728*I)*c^7*k0 - 8428*c^6*k0^2 + (5040*I)*c^5*k0^3 + 1750*c^4*k0^4 - (336*I)*c^3*k0^5 - 28*c^2*k0^6))/(64*k0^2), 0, (-11*(28501*c^10 - (93300*I)*c^9*k0 - 136125*c^8*k0^2 + (115920*I)*c^7*k0^3 + 63210*c^6*k0^4 - (22680*I)*c^5*k0^5 - 5250*c^4*k0^6 + (720*I)*c^3*k0^7 + 45*c^2*k0^8))/(128*k0^2)}, 2, 11, 1]

besseltransforms/2-2-4

@@ -0,0 +1,2 @@
+-(2*k^2*(-2 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 4*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 2*k^2*(-2 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 4*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4)/(2*k^4*k0^2)
+SeriesData[k, Infinity, {(4*c^2)/k0^2, (-30*c^3)/k0^2 + ((15*I)*c^2)/k0, -24*c^2 + (100*c^4)/k0^2 - ((96*I)*c^3)/k0, 105*c^3 - (315*c^5)/(2*k0^2) + ((875*I)/4*c^4)/k0 - (35*I)/2*c^2*k0, 0, (21*(138*c^7 - (301*I)*c^6*k0 - 270*c^5*k0^2 + (125*I)*c^4*k0^3 + 30*c^3*k0^4 - (3*I)*c^2*k0^5))/(8*k0^2), 0, (-33*(3110*c^9 - (9075*I)*c^8*k0 - 11592*c^7*k0^2 + (8428*I)*c^6*k0^3 + 3780*c^5*k0^4 - (1050*I)*c^4*k0^5 - 168*c^3*k0^6 + (12*I)*c^2*k0^7))/(64*k0^2)}, 2, 11, 1]

besseltransforms/2-2-5

@@ -0,0 +1,2 @@
+(-2*(k^4*(-5 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5) + k^4*(-5 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + k^4*(-5 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5)/(5*k^5*k0^2)
+SeriesData[k, Infinity, {(5*c^2)/k0^2, (-24*(2*c^3 - I*c^2*k0))/k0^2, (35*(25*c^4 - (24*I)*c^3*k0 - 6*c^2*k0^2))/(4*k0^2), (-32*(18*c^5 - (25*I)*c^4*k0 - 12*c^3*k0^2 + (2*I)*c^2*k0^3))/k0^2, (21*(301*c^6 - (540*I)*c^5*k0 - 375*c^4*k0^2 + (120*I)*c^3*k0^3 + 15*c^2*k0^4))/(8*k0^2), 0, ((-165*(c - I*k0)^8)/128 + (165*(2*c - I*k0)^8)/64 - (165*(3*c - I*k0)^8)/128)/(5*k0^2), 0, ((143*(c - I*k0)^10)/256 - (143*(2*c - I*k0)^10)/128 + (143*(3*c - I*k0)^10)/256)/(5*k0^2)}, 2, 11, 1]

besseltransforms/2-2-6

@@ -0,0 +1,2 @@
+(-3*k^4*(-3 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 8*k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 + 6*k^4*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^2*(-3 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 32*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 - 3*k^4*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 8*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6)/(3*k^6*k0^2)
+SeriesData[k, Infinity, {(6*c^2)/k0^2, (-35*(2*c^3 - I*c^2*k0))/k0^2, (16*(25*c^4 - (24*I)*c^3*k0 - 6*c^2*k0^2))/k0^2, (-315*(18*c^5 - (25*I)*c^4*k0 - 12*c^3*k0^2 + (2*I)*c^2*k0^3))/(4*k0^2), (16*(c - I*k0)^6 - 32*(2*c - I*k0)^6 + 16*(3*c - I*k0)^6)/(3*k0^2), ((-99*(c - I*k0)^7)/16 + (99*(2*c - I*k0)^7)/8 - (99*(3*c - I*k0)^7)/16)/(3*k0^2), 0, ((143*(c - I*k0)^9)/128 - (143*(2*c - I*k0)^9)/64 + (143*(3*c - I*k0)^9)/128)/(3*k0^2)}, 2, 11, 1]

besseltransforms/2-2-7

@@ -0,0 +1,2 @@
+(-2*(k^6*(-7 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7) + k^6*(-7 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7 + k^6*(-7 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7)/(7*k^7*k0^2)
+SeriesData[k, Infinity, {(7*c^2)/k0^2, (-48*(2*c^3 - I*c^2*k0))/k0^2, (105*(25*c^4 - (24*I)*c^3*k0 - 6*c^2*k0^2))/(4*k0^2), (-160*(18*c^5 - (25*I)*c^4*k0 - 12*c^3*k0^2 + (2*I)*c^2*k0^3))/k0^2, (231*(301*c^6 - (540*I)*c^5*k0 - 375*c^4*k0^2 + (120*I)*c^3*k0^3 + 15*c^2*k0^4))/(8*k0^2), (-64*(c - I*k0)^7 + 128*(2*c - I*k0)^7 - 64*(3*c - I*k0)^7)/(7*k0^2), ((3003*(c - I*k0)^8)/128 - (3003*(2*c - I*k0)^8)/64 + (3003*(3*c - I*k0)^8)/128)/(7*k0^2), 0, ((-1001*(c - I*k0)^10)/256 + (1001*(2*c - I*k0)^10)/128 - (1001*(3*c - I*k0)^10)/256)/(7*k0^2)}, 2, 11, 1]

besseltransforms/2-3-1

@@ -0,0 +1,9 @@
+Integrate[(E^(I*k0*x)*(-1 + E^(-(c*x)))^2*BesselJ[1, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 1 && q == 3 && κ == 2]
+
+                                -2 c x + I k0 x        c x 2                                    2  2              4  4              6  6               8  8      Pi                                         2  2               4  4              6  6               8  8      Pi
+                             -(E                (-1 + E   )  (8 k x (-14783093325 + 1452971520 k  x  - 309657600 k  x  + 251658240 k  x  + 2147483648 k  x ) Cos[-- + k x] - 3 (156043762875 - 11416204800 k  x  + 1589575680 k  x  - 587202560 k  x  + 2147483648 k  x ) Sin[-- + k x]))
+                                                                                                                                                                 4                                                                                                            4
+Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}.
+                                                                                                                                                    19/2   3             23/2
+                                                                                                                                        8589934592 k     k0  Sqrt[2 Pi] x
+Series[Integrate[(E^(I*k0*x)*(-1 + E^(-(c*x)))^2*BesselJ[1, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 1 && q == 3 && κ == 2], {k, Infinity, 10}]

besseltransforms/2-3-2

@@ -0,0 +1,2 @@
+(-4*(-3 + 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) - (8*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3)/k^2 + 2*(-3 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + (4*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3)/k^2 + 3*k0*Sqrt[Pi]*(Piecewise[{{0, k^2/k0^2 <= 1}}, (4*(k^2 - k0^2)^(3/2))/(3*k^2*k0*Sqrt[Pi])] + I*Piecewise[{{(-2*(2*k0*(k0 - Sqrt[-k^2 + k0^2]) + k^2*(-3 + (2*Sqrt[-k^2 + k0^2])/k0)))/(3*k^2*Sqrt[Pi]), k^2/k0^2 < 1}, {(2*(1 - (2*k0^2)/(3*k^2)))/Sqrt[Pi], k^2/k0^2 > 1}}, 0]))/(12*k0^3)
+SeriesData[k, Infinity, {c^2/k0^3, (-2*(c^3 - I*c^2*k0))/k0^3, (7*c^4 - (12*I)*c^3*k0 - 6*c^2*k0^2)/(4*k0^3), 0, (-31*c^6 + (90*I)*c^5*k0 + 105*c^4*k0^2 - (60*I)*c^3*k0^3 - 15*c^2*k0^4)/(24*k0^3), 0, (127*c^8 - (504*I)*c^7*k0 - 868*c^6*k0^2 + (840*I)*c^5*k0^3 + 490*c^4*k0^4 - (168*I)*c^3*k0^5 - 28*c^2*k0^6)/(64*k0^3), 0, (-511*c^10 + (2550*I)*c^9*k0 + 5715*c^8*k0^2 - (7560*I)*c^7*k0^3 - 6510*c^6*k0^4 + (3780*I)*c^5*k0^5 + 1470*c^4*k0^6 - (360*I)*c^3*k0^7 - 45*c^2*k0^8)/(128*k0^3)}, 1, 11, 1]

besseltransforms/2-3-3

@@ -0,0 +1,2 @@
+(k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 2*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 2*k^2*(-3 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 4*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 2*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4)/(6*k^3*k0^3)
+SeriesData[k, Infinity, {c^2/k0^3, (-3*(2*c^3 - I*c^2*k0))/k0^3, (2*(25*c^4 - (24*I)*c^3*k0 - 6*c^2*k0^2))/(3*k0^3), (-5*(18*c^5 - (25*I)*c^4*k0 - 12*c^3*k0^2 + (2*I)*c^2*k0^3))/(4*k0^3), 0, ((c - I*k0)^7/8 - (2*c - I*k0)^7/4 + (3*c - I*k0)^7/8)/(6*k0^3), 0, ((-3*(c - I*k0)^9)/64 + (3*(2*c - I*k0)^9)/32 - (3*(3*c - I*k0)^9)/64)/(6*k0^3), 0, ((3*(c - I*k0)^11)/128 - (3*(2*c - I*k0)^11)/64 + (3*(3*c - I*k0)^11)/128)/(6*k0^3)}, 1, 11, 1]

besseltransforms/2-3-4

@@ -0,0 +1,2 @@
+(-2*(k^4*(-15 + 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5) + k^4*(-15 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + k^4*(-15 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5)/(60*k^4*k0^3)
+SeriesData[k, Infinity, {c^2/k0^3, (-4*(2*c^3 - I*c^2*k0))/k0^3, (5*(25*c^4 - (24*I)*c^3*k0 - 6*c^2*k0^2))/(4*k0^3), (-4*(18*c^5 - (25*I)*c^4*k0 - 12*c^3*k0^2 + (2*I)*c^2*k0^3))/k0^3, (7*(301*c^6 - (540*I)*c^5*k0 - 375*c^4*k0^2 + (120*I)*c^3*k0^3 + 15*c^2*k0^4))/(24*k0^3), 0, ((-45*(c - I*k0)^8)/32 + (45*(2*c - I*k0)^8)/16 - (45*(3*c - I*k0)^8)/32)/(60*k0^3), 0, ((33*(c - I*k0)^10)/64 - (33*(2*c - I*k0)^10)/32 + (33*(3*c - I*k0)^10)/64)/(60*k0^3)}, 1, 11, 1]

besseltransforms/2-3-5

@@ -0,0 +1,2 @@
+(6*k^4*(5 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 4*k^2*(15 - 11*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 + 12*k^4*(-5 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 8*k^2*(-15 + 11*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 + 6*k^4*(5 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 4*k^2*(15 - 11*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6)/(60*k^5*k0^3)
+SeriesData[k, Infinity, {c^2/k0^3, (-5*(2*c^3 - I*c^2*k0))/k0^3, (2*(25*c^4 - (24*I)*c^3*k0 - 6*c^2*k0^2))/k0^3, (-35*(18*c^5 - (25*I)*c^4*k0 - 12*c^3*k0^2 + (2*I)*c^2*k0^3))/(4*k0^3), (32*(c - I*k0)^6 - 64*(2*c - I*k0)^6 + 32*(3*c - I*k0)^6)/(60*k0^3), ((-45*(c - I*k0)^7)/4 + (45*(2*c - I*k0)^7)/2 - (45*(3*c - I*k0)^7)/4)/(60*k0^3), 0, ((55*(c - I*k0)^9)/32 - (55*(2*c - I*k0)^9)/16 + (55*(3*c - I*k0)^9)/32)/(60*k0^3), 0, ((-39*(c - I*k0)^11)/64 + (39*(2*c - I*k0)^11)/32 - (39*(3*c - I*k0)^11)/64)/(60*k0^3)}, 1, 11, 1]

besseltransforms/2-3-6

@@ -0,0 +1,2 @@
+(-2*(k^6*(-35 + 6*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7) + k^6*(-35 + 6*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7 + k^6*(-35 + 6*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7)/(210*k^6*k0^3)
+SeriesData[k, Infinity, {c^2/k0^3, (-6*(2*c^3 - I*c^2*k0))/k0^3, (35*(25*c^4 - (24*I)*c^3*k0 - 6*c^2*k0^2))/(12*k0^3), (-16*(18*c^5 - (25*I)*c^4*k0 - 12*c^3*k0^2 + (2*I)*c^2*k0^3))/k0^3, (21*(301*c^6 - (540*I)*c^5*k0 - 375*c^4*k0^2 + (120*I)*c^3*k0^3 + 15*c^2*k0^4))/(8*k0^3), (-160*(c - I*k0)^7 + 320*(2*c - I*k0)^7 - 160*(3*c - I*k0)^7)/(210*k0^3), ((3465*(c - I*k0)^8)/64 - (3465*(2*c - I*k0)^8)/32 + (3465*(3*c - I*k0)^8)/64)/(210*k0^3), 0, ((-1001*(c - I*k0)^10)/128 + (1001*(2*c - I*k0)^10)/64 - (1001*(3*c - I*k0)^10)/128)/(210*k0^3)}, 1, 11, 1]

besseltransforms/2-3-7

@@ -0,0 +1,2 @@
+((7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^8)/(336*k^7) - (7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^8)/(168*k^7) + (7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^8)/(336*k^7))/k0^3
+SeriesData[k, Infinity, {c^2/k0^3, (-7*(2*c^3 - I*c^2*k0))/k0^3, (4*(25*c^4 - (24*I)*c^3*k0 - 6*c^2*k0^2))/k0^3, (-105*(18*c^5 - (25*I)*c^4*k0 - 12*c^3*k0^2 + (2*I)*c^2*k0^3))/(4*k0^3), (16*(301*c^6 - (540*I)*c^5*k0 - 375*c^4*k0^2 + (120*I)*c^3*k0^3 + 15*c^2*k0^4))/(3*k0^3), ((-33*(c - I*k0)^7)/16 + (33*(2*c - I*k0)^7)/8 - (33*(3*c - I*k0)^7)/16)/k0^3, ((8*(c - I*k0)^8)/7 - (16*(2*c - I*k0)^8)/7 + (8*(3*c - I*k0)^8)/7)/k0^3, ((-143*(c - I*k0)^9)/384 + (143*(2*c - I*k0)^9)/192 - (143*(3*c - I*k0)^9)/384)/k0^3, 0, ((13*(c - I*k0)^11)/256 - (13*(2*c - I*k0)^11)/128 + (13*(3*c - I*k0)^11)/256)/k0^3}, 1, 11, 1]

besseltransforms/3-1-2.REMOVED.git-id

@@ -0,0 +1 @@
+9a2ec0ef6771d8a7db72ddc960cbd1172c4c24e2

besseltransforms/3-2-1

@@ -0,0 +1,2 @@
+(-6*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 6*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) - 2*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + k*Sqrt[Pi]*(Piecewise[{{0, k^2/k0^2 <= 1}}, (2*Sqrt[k^2 - k0^2])/(k*Sqrt[Pi])] + I*Piecewise[{{(2*k0)/(k*Sqrt[Pi]), k0^2/k^2 < 1}, {(2*(k0 - Sqrt[-k^2 + k0^2]))/(k*Sqrt[Pi]), k0^2/k^2 > 1}}, 0]))/(2*k*k0^2)
+Piecewise[{{SeriesData[k, Infinity, {(9*c^4)/(2*k0^2) - ((3*I)*c^3)/k0, 0, (-15*(9*c^6 - (15*I)*c^5*k0 - 9*c^4*k0^2 + (2*I)*c^3*k0^3))/(4*k0^2), 0, (105*(69*c^8 - (172*I)*c^7*k0 - 180*c^6*k0^2 + (100*I)*c^5*k0^3 + 30*c^4*k0^4 - (4*I)*c^3*k0^5))/(32*k0^2), 0, (-105*(933*c^10 - (3025*I)*c^9*k0 - 4347*c^8*k0^2 + (3612*I)*c^7*k0^3 + 1890*c^6*k0^4 - (630*I)*c^5*k0^5 - 126*c^4*k0^6 + (12*I)*c^3*k0^7))/(64*k0^2)}, 4, 11, 1], (k0 <= 0 && k^2/k0^2 > 1) || k0 > 0}}, SeriesData[k, Infinity, {-k0^(-2), 0, 1/2, 0, ((3*c*(c - I*k0)^3)/8 - (3*c*(2*c - I*k0)^3)/4 + (3*c*(3*c - I*k0)^3)/8 - (3*I)/8*(c - I*k0)^3*k0 + (3*I)/8*(2*c - I*k0)^3*k0 - I/8*(3*c - I*k0)^3*k0)/k0^2, 0, ((-3*c*(c - I*k0)^5)/16 + (3*c*(2*c - I*k0)^5)/8 - (3*c*(3*c - I*k0)^5)/16 + (3*I)/16*(c - I*k0)^5*k0 - (3*I)/16*(2*c - I*k0)^5*k0 + I/16*(3*c - I*k0)^5*k0)/k0^2, 0, ((15*c*(c - I*k0)^7)/128 - (15*c*(2*c - I*k0)^7)/64 + (15*c*(3*c - I*k0)^7)/128 - (15*I)/128*(c - I*k0)^7*k0 + (15*I)/128*(2*c - I*k0)^7*k0 - (5*I)/128*(3*c - I*k0)^7*k0)/k0^2, 0, ((-21*c*(c - I*k0)^9)/256 + (21*c*(2*c - I*k0)^9)/128 - (21*c*(3*c - I*k0)^9)/256 + (21*I)/256*(c - I*k0)^9*k0 - (21*I)/256*(2*c - I*k0)^9*k0 + (7*I)/256*(3*c - I*k0)^9*k0)/k0^2}, 0, 11, 1]]

besseltransforms/3-2-2

@@ -0,0 +1,2 @@
+(-1 + (6*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2)/k^2 - (6*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2)/k^2 + (2*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2)/k^2 + Sqrt[Pi]*(I*Piecewise[{{0, k^2/k0^2 <= 1}}, (2*k0*Sqrt[k^2 - k0^2])/(k^2*Sqrt[Pi])] + Piecewise[{{(k^2 + 2*k0*(-k0 + Sqrt[-k^2 + k0^2]))/(k^2*Sqrt[Pi]), k^2/k0^2 < 1}, {(1 - (2*k0^2)/k^2)/Sqrt[Pi], k^2/k0^2 > 1}}, 0]))/(2*k0^2)
+SeriesData[k, Infinity, {(3*c^3)/k0^2, 0, (-15*(5*c^5 - (6*I)*c^4*k0 - 2*c^3*k0^2))/(4*k0^2), 0, (21*(43*c^7 - (90*I)*c^6*k0 - 75*c^5*k0^2 + (30*I)*c^4*k0^3 + 5*c^3*k0^4))/(8*k0^2), 0, (-15*(3025*c^9 - (8694*I)*c^8*k0 - 10836*c^7*k0^2 + (7560*I)*c^6*k0^3 + 3150*c^5*k0^4 - (756*I)*c^4*k0^5 - 84*c^3*k0^6))/(64*k0^2)}, 3, 11, 1]

besseltransforms/3-3-1

@@ -0,0 +1,9 @@
+Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^3*BesselJ[1, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 1 && q == 3 && κ == 3]
+
+                                -3 c x + I k0 x        c x 3                                    2  2              4  4              6  6               8  8      Pi                                         2  2               4  4              6  6               8  8      Pi
+                             -(E                (-1 + E   )  (8 k x (-14783093325 + 1452971520 k  x  - 309657600 k  x  + 251658240 k  x  + 2147483648 k  x ) Cos[-- + k x] - 3 (156043762875 - 11416204800 k  x  + 1589575680 k  x  - 587202560 k  x  + 2147483648 k  x ) Sin[-- + k x]))
+                                                                                                                                                                 4                                                                                                            4
+Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}.
+                                                                                                                                                    19/2   3             23/2
+                                                                                                                                        8589934592 k     k0  Sqrt[2 Pi] x
+Series[Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^3*BesselJ[1, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 1 && q == 3 && κ == 3], {k, Infinity, 10}]

besseltransforms/3-3-2

@@ -0,0 +1,2 @@
+(6*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) - (12*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3)/k^2 + 6*(-3 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + (12*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3)/k^2 + 2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) - (4*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3)/k^2 + 3*k0*Sqrt[Pi]*(Piecewise[{{0, k^2/k0^2 <= 1}}, (4*(k^2 - k0^2)^(3/2))/(3*k^2*k0*Sqrt[Pi])] + I*Piecewise[{{(-2*(2*k0*(k0 - Sqrt[-k^2 + k0^2]) + k^2*(-3 + (2*Sqrt[-k^2 + k0^2])/k0)))/(3*k^2*Sqrt[Pi]), k^2/k0^2 < 1}, {(2*(1 - (2*k0^2)/(3*k^2)))/Sqrt[Pi], k^2/k0^2 > 1}}, 0]))/(12*k0^3)
+SeriesData[k, Infinity, {(2*c^3)/k0^3, (-9*c^4)/(2*k0^3) + ((3*I)*c^3)/k0^2, 0, (5*(9*c^6 - (15*I)*c^5*k0 - 9*c^4*k0^2 + (2*I)*c^3*k0^3))/(4*k0^3), 0, (-21*(69*c^8 - (172*I)*c^7*k0 - 180*c^6*k0^2 + (100*I)*c^5*k0^3 + 30*c^4*k0^4 - (4*I)*c^3*k0^5))/(32*k0^3), 0, (15*(933*c^10 - (3025*I)*c^9*k0 - 4347*c^8*k0^2 + (3612*I)*c^7*k0^3 + 1890*c^6*k0^4 - (630*I)*c^5*k0^5 - 126*c^4*k0^6 + (12*I)*c^3*k0^7))/(64*k0^3)}, 2, 11, 1]

besseltransforms/3-3-3

@@ -0,0 +1,2 @@
+(k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 2*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 3*k^2*(-3 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 6*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 3*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 6*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + k^2*(-3 + 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 2*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4)/(6*k^3*k0^3)
+SeriesData[k, Infinity, {(3*c^3)/k0^3, (-20*c^4)/k0^3 + ((8*I)*c^3)/k0^2, (15*(13*c^5 - (10*I)*c^4*k0 - 2*c^3*k0^2))/(4*k0^3), 0, (-7*(243*c^7 - (350*I)*c^6*k0 - 195*c^5*k0^2 + (50*I)*c^4*k0^3 + 5*c^3*k0^4))/(8*k0^3), 0, (3*(34105*c^9 - (69930*I)*c^8*k0 - 61236*c^7*k0^2 + (29400*I)*c^6*k0^3 + 8190*c^5*k0^4 - (1260*I)*c^4*k0^5 - 84*c^3*k0^6))/(64*k0^3), 0, (-33*(55591*c^11 - (145750*I)*c^10*k0 - 170525*c^9*k0^2 + (116550*I)*c^8*k0^3 + 51030*c^7*k0^4 - (14700*I)*c^6*k0^5 - 2730*c^5*k0^6 + (300*I)*c^4*k0^7 + 15*c^3*k0^8))/(128*k0^3)}, 2, 11, 1]

besseltransforms/3-3-4

@@ -0,0 +1,2 @@
+(-3*(k^4*(-15 + 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5) + 3*(k^4*(-15 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5) + k^4*(-15 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 - k^4*(-15 + 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) - 4*k^2*(-10 + 7*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 - 24*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5)/(60*k^4*k0^3)
+SeriesData[k, Infinity, {(4*c^3)/k0^3, (-75*c^4)/(2*k0^3) + ((15*I)*c^3)/k0^2, (156*c^5)/k0^3 - ((120*I)*c^4)/k0^2 - (24*c^3)/k0, (-35*(35*c^6 - (39*I)*c^5*k0 - 15*c^4*k0^2 + (2*I)*c^3*k0^3))/(4*k0^3), 0, (63*(555*c^8 - (972*I)*c^7*k0 - 700*c^6*k0^2 + (260*I)*c^5*k0^3 + 50*c^4*k0^4 - (4*I)*c^3*k0^5))/(32*k0^3), 0, (-33*(14575*c^10 - (34105*I)*c^9*k0 - 34965*c^8*k0^2 + (20412*I)*c^7*k0^3 + 7350*c^6*k0^4 - (1638*I)*c^5*k0^5 - 210*c^4*k0^6 + (12*I)*c^3*k0^7))/(64*k0^3)}, 2, 11, 1]

besseltransforms/3-3-5

@@ -0,0 +1,2 @@
+(3*k^4*(5 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 2*k^2*(15 - 11*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 + 9*k^4*(-5 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 6*k^2*(-15 + 11*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 48*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 + 9*k^4*(5 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 6*k^2*(15 - 11*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 48*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 + 3*k^4*(-5 + 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 2*k^2*(-15 + 11*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6)/(30*k^5*k0^3)
+SeriesData[k, Infinity, {(5*c^3)/k0^3, (-12*(5*c^4 - (2*I)*c^3*k0))/k0^3, (105*(13*c^5 - (10*I)*c^4*k0 - 2*c^3*k0^2))/(4*k0^3), (-32*(35*c^6 - (39*I)*c^5*k0 - 15*c^4*k0^2 + (2*I)*c^3*k0^3))/k0^3, (63*(243*c^7 - (350*I)*c^6*k0 - 195*c^5*k0^2 + (50*I)*c^4*k0^3 + 5*c^3*k0^4))/(8*k0^3), 0, (-11*(34105*c^9 - (69930*I)*c^8*k0 - 61236*c^7*k0^2 + (29400*I)*c^6*k0^3 + 8190*c^5*k0^4 - (1260*I)*c^4*k0^5 - 84*c^3*k0^6))/(64*k0^3), 0, ((-39*(c - I*k0)^11)/128 + (117*(2*c - I*k0)^11)/128 - (117*(3*c - I*k0)^11)/128 + (39*(4*c - I*k0)^11)/128)/(30*k0^3)}, 2, 11, 1]

besseltransforms/3-3-6

@@ -0,0 +1,2 @@
+(-3*(k^6*(-35 + 6*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7) + 3*(k^6*(-35 + 6*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7) + k^6*(-35 + 6*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7 - k^6*(-35 + 6*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) - 6*k^4*(-35 + 17*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 - 16*k^2*(-21 + 16*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 - 160*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7)/(210*k^6*k0^3)
+SeriesData[k, Infinity, {(6*c^3)/k0^3, (-35*(5*c^4 - (2*I)*c^3*k0))/(2*k0^3), (48*(13*c^5 - (10*I)*c^4*k0 - 2*c^3*k0^2))/k0^3, (-315*(35*c^6 - (39*I)*c^5*k0 - 15*c^4*k0^2 + (2*I)*c^3*k0^3))/(4*k0^3), (32*(243*c^7 - (350*I)*c^6*k0 - 195*c^5*k0^2 + (50*I)*c^4*k0^3 + 5*c^3*k0^4))/k0^3, (-693*(555*c^8 - (972*I)*c^7*k0 - 700*c^6*k0^2 + (260*I)*c^5*k0^3 + 50*c^4*k0^4 - (4*I)*c^3*k0^5))/(32*k0^3), 0, ((-1001*(c - I*k0)^10)/128 + (3003*(2*c - I*k0)^10)/128 - (3003*(3*c - I*k0)^10)/128 + (1001*(4*c - I*k0)^10)/128)/(210*k0^3)}, 2, 11, 1]

besseltransforms/3-3-7

@@ -0,0 +1,2 @@
+((7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^8)/(336*k^7) - (7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^8)/(112*k^7) + (7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^8)/(112*k^7) - (7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^8)/(336*k^7))/k0^3
+SeriesData[k, Infinity, {(7*c^3)/k0^3, (-24*(5*c^4 - (2*I)*c^3*k0))/k0^3, (315*(13*c^5 - (10*I)*c^4*k0 - 2*c^3*k0^2))/(4*k0^3), (-160*(35*c^6 - (39*I)*c^5*k0 - 15*c^4*k0^2 + (2*I)*c^3*k0^3))/k0^3, (693*(243*c^7 - (350*I)*c^6*k0 - 195*c^5*k0^2 + (50*I)*c^4*k0^3 + 5*c^3*k0^4))/(8*k0^3), (-96*(555*c^8 - (972*I)*c^7*k0 - 700*c^6*k0^2 + (260*I)*c^5*k0^3 + 50*c^4*k0^4 - (4*I)*c^3*k0^5))/k0^3, ((-143*(c - I*k0)^9)/384 + (143*(2*c - I*k0)^9)/128 - (143*(3*c - I*k0)^9)/128 + (143*(4*c - I*k0)^9)/384)/k0^3, 0, ((13*(c - I*k0)^11)/256 - (39*(2*c - I*k0)^11)/256 + (39*(3*c - I*k0)^11)/256 - (13*(4*c - I*k0)^11)/256)/k0^3}, 2, 11, 1]

besseltransforms/4-1-0.REMOVED.git-id

@@ -0,0 +1 @@
+bee84490a2f9b473adccfa023c6611be883a01a7

besseltransforms/4-1-1.REMOVED.git-id

@@ -0,0 +1 @@
+a9ad81536da843935e33ae577308937e51c35ca7

besseltransforms/4-1-2.REMOVED.git-id

@@ -0,0 +1 @@
+8640f89aa7c80f216e563672dd2763f2c7becbce

besseltransforms/4-1-3

@@ -0,0 +1,2 @@
+((k^2*(-3 + Sqrt[1 + k^2/(c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2)/(k^3*Sqrt[1 + k^2/(c - I*k0)^2]) - (4*(k^2*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(2*c - I*k0)^2]) + (6*(k^2*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(3*c - I*k0)^2]) - (4*(k^2*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(4*c - I*k0)^2]) + (k^2*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2)/(k^3*Sqrt[1 + k^2/(5*c - I*k0)^2]))/k0
+SeriesData[k, Infinity, {((-105*I)*c^4)/k + (315*c^5)/(k*k0), 0, (-945*(30*c^7 - (28*I)*c^6*k0 - 9*c^5*k0^2 + I*c^4*k0^3))/(2*k*k0), 0, (3465*(2025*c^9 - (2979*I)*c^8*k0 - 1800*c^7*k0^2 + (560*I)*c^6*k0^3 + 90*c^5*k0^4 - (6*I)*c^4*k0^5))/(16*k*k0)}, 5, 11, 1]

besseltransforms/4-1-4

@@ -0,0 +1,2 @@
+((k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4)/(k^4*Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) - (4*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) + (6*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)) - (4*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(4*c - I*k0)^2]*(4*c - I*k0)) + (k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4)/(k^4*Sqrt[1 + k^2/(5*c - I*k0)^2]*(5*c - I*k0)))/k0
+SeriesData[k, Infinity, {(105*c^4)/(k*k0), 0, (-315*(28*c^6 - (18*I)*c^5*k0 - 3*c^4*k0^2))/(2*k*k0), 0, (2079*(993*c^8 - (1200*I)*c^7*k0 - 560*c^6*k0^2 + (120*I)*c^5*k0^3 + 10*c^4*k0^4))/(16*k*k0), 0, (-2145*(49346*c^10 - (85050*I)*c^9*k0 - 62559*c^8*k0^2 + (25200*I)*c^7*k0^3 + 5880*c^6*k0^4 - (756*I)*c^5*k0^5 - 42*c^4*k0^6))/(32*k*k0)}, 4, 11, 1]

besseltransforms/4-1-5

@@ -0,0 +1,2 @@
+((k^4*(-5 + Sqrt[1 + k^2/(c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4)/(k^5*Sqrt[1 + k^2/(c - I*k0)^2]) - (4*(k^4*(-5 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(2*c - I*k0)^2]) + (6*(k^4*(-5 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(3*c - I*k0)^2]) - (4*(k^4*(-5 + Sqrt[1 + k^2/(4*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(4*c - I*k0)^2]) + (k^4*(-5 + Sqrt[1 + k^2/(5*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4)/(k^5*Sqrt[1 + k^2/(5*c - I*k0)^2]))/k0
+SeriesData[k, Infinity, {(384*c^4)/(k*k0), ((945*I)*c^4)/k - (2835*c^5)/(k*k0), 0, (3465*(30*c^7 - (28*I)*c^6*k0 - 9*c^5*k0^2 + I*c^4*k0^3))/(2*k*k0), 0, (-9009*(2025*c^9 - (2979*I)*c^8*k0 - 1800*c^7*k0^2 + (560*I)*c^6*k0^3 + 90*c^5*k0^4 - (6*I)*c^4*k0^5))/(16*k*k0)}, 4, 11, 1]

besseltransforms/4-1-6

@@ -0,0 +1,2 @@
+((k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(k^6*Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) - (4*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6))/(k^6*Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) + (6*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6))/(k^6*Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)) - (4*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6))/(k^6*Sqrt[1 + k^2/(4*c - I*k0)^2]*(4*c - I*k0)) + (k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6)/(k^6*Sqrt[1 + k^2/(5*c - I*k0)^2]*(5*c - I*k0)))/k0
+SeriesData[k, Infinity, {(945*c^4)/(k*k0), ((3840*I)*c^4)/k - (11520*c^5)/(k*k0), (3465*(28*c^6 - (18*I)*c^5*k0 - 3*c^4*k0^2))/(2*k*k0), 0, (-9009*(993*c^8 - (1200*I)*c^7*k0 - 560*c^6*k0^2 + (120*I)*c^5*k0^3 + 10*c^4*k0^4))/(16*k*k0), 0, (6435*(49346*c^10 - (85050*I)*c^9*k0 - 62559*c^8*k0^2 + (25200*I)*c^7*k0^3 + 5880*c^6*k0^4 - (756*I)*c^5*k0^5 - 42*c^4*k0^6))/(32*k*k0)}, 4, 11, 1]

besseltransforms/4-1-7

@@ -0,0 +1,2 @@
+((k^6*(-7 + Sqrt[1 + k^2/(c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(k^7*Sqrt[1 + k^2/(c - I*k0)^2]) - (4*(k^6*(-7 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6))/(k^7*Sqrt[1 + k^2/(2*c - I*k0)^2]) + (6*(k^6*(-7 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6))/(k^7*Sqrt[1 + k^2/(3*c - I*k0)^2]) - (4*(k^6*(-7 + Sqrt[1 + k^2/(4*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6))/(k^7*Sqrt[1 + k^2/(4*c - I*k0)^2]) + (k^6*(-7 + Sqrt[1 + k^2/(5*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6)/(k^7*Sqrt[1 + k^2/(5*c - I*k0)^2]))/k0
+SeriesData[k, Infinity, {(1920*c^4)/(k*k0), ((10395*I)*c^4)/k - (31185*c^5)/(k*k0), (7680*(28*c^6 - (18*I)*c^5*k0 - 3*c^4*k0^2))/(k*k0), (-45045*(30*c^7 - (28*I)*c^6*k0 - 9*c^5*k0^2 + I*c^4*k0^3))/(2*k*k0), 0, (45045*(2025*c^9 - (2979*I)*c^8*k0 - 1800*c^7*k0^2 + (560*I)*c^6*k0^3 + 90*c^5*k0^4 - (6*I)*c^4*k0^5))/(16*k*k0)}, 4, 11, 1]

besseltransforms/4-2-0

@@ -0,0 +1 @@
+Integrate[(E^(I*k0*x)*(-1 + E^(-(c*x)))^4*BesselJ[0, k*x])/(k0^2*x), {x, 0, Infinity}, Assumptions -> n == 0 && q == 2 && κ == 4]

besseltransforms/4-2-1

@@ -0,0 +1,2 @@
+((-4*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0))/k + (6*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0))/k - (4*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0))/k + ((-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0))/k + (Sqrt[Pi]*(Piecewise[{{0, k^2/k0^2 <= 1}}, (2*Sqrt[k^2 - k0^2])/(k*Sqrt[Pi])] + I*Piecewise[{{(2*k0)/(k*Sqrt[Pi]), k0^2/k^2 < 1}, {(2*(k0 - Sqrt[-k^2 + k0^2]))/(k*Sqrt[Pi]), k0^2/k^2 > 1}}, 0]))/2)/k0^2
+Piecewise[{{SeriesData[k, Infinity, {(-3*c^4)/k0^2, 0, (-45*c^4)/2 + (195*c^6)/(2*k0^2) - ((90*I)*c^5)/k0, 0, (6825*c^6)/4 - (25515*c^8)/(16*k0^2) + ((2625*I)*c^7)/k0 - (525*I)*c^5*k0 - (525*c^4*k0^2)/8, 0, (105*(6821*c^10 - (15540*I)*c^9*k0 - 15309*c^8*k0^2 + (8400*I)*c^7*k0^3 + 2730*c^6*k0^4 - (504*I)*c^5*k0^5 - 42*c^4*k0^6))/(32*k0^2)}, 4, 11, 1], (k0 <= 0 && k^2/k0^2 > 1) || k0 > 0}}, SeriesData[k, Infinity, {-k0^(-2), 0, 1/2, 0, ((c*(c - I*k0)^3)/2 - (3*c*(2*c - I*k0)^3)/2 + (3*c*(3*c - I*k0)^3)/2 - (c*(4*c - I*k0)^3)/2 - I/2*(c - I*k0)^3*k0 + (3*I)/4*(2*c - I*k0)^3*k0 - I/2*(3*c - I*k0)^3*k0 + I/8*(4*c - I*k0)^3*k0)/k0^2, 0, (-(c*(c - I*k0)^5)/4 + (3*c*(2*c - I*k0)^5)/4 - (3*c*(3*c - I*k0)^5)/4 + (c*(4*c - I*k0)^5)/4 + I/4*(c - I*k0)^5*k0 - (3*I)/8*(2*c - I*k0)^5*k0 + I/4*(3*c - I*k0)^5*k0 - I/16*(4*c - I*k0)^5*k0)/k0^2, 0, ((5*c*(c - I*k0)^7)/32 - (15*c*(2*c - I*k0)^7)/32 + (15*c*(3*c - I*k0)^7)/32 - (5*c*(4*c - I*k0)^7)/32 - (5*I)/32*(c - I*k0)^7*k0 + (15*I)/64*(2*c - I*k0)^7*k0 - (5*I)/32*(3*c - I*k0)^7*k0 + (5*I)/128*(4*c - I*k0)^7*k0)/k0^2, 0, ((-7*c*(c - I*k0)^9)/64 + (21*c*(2*c - I*k0)^9)/64 - (21*c*(3*c - I*k0)^9)/64 + (7*c*(4*c - I*k0)^9)/64 + (7*I)/64*(c - I*k0)^9*k0 - (21*I)/128*(2*c - I*k0)^9*k0 + (7*I)/64*(3*c - I*k0)^9*k0 - (7*I)/256*(4*c - I*k0)^9*k0)/k0^2}, 0, 11, 1]]

besseltransforms/4-2-2

@@ -0,0 +1,2 @@
+(-k^2 + 8*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 12*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 8*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 2*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + k^2*Sqrt[Pi]*(I*Piecewise[{{0, k^2/k0^2 <= 1}}, (2*k0*Sqrt[k^2 - k0^2])/(k^2*Sqrt[Pi])] + Piecewise[{{(k^2 + 2*k0*(-k0 + Sqrt[-k^2 + k0^2]))/(k^2*Sqrt[Pi]), k^2/k0^2 < 1}, {(1 - (2*k0^2)/k^2)/Sqrt[Pi], k^2/k0^2 > 1}}, 0]))/(2*k^2*k0^2)
+SeriesData[k, Infinity, {(30*c^5)/k0^2 - ((15*I)*c^4)/k0, 0, 315*c^5 - (525*c^7)/k0^2 + ((1365*I)/2*c^6)/k0 - (105*I)/2*c^4*k0, 0, (315*(370*c^9 - (729*I)*c^8*k0 - 600*c^7*k0^2 + (260*I)*c^6*k0^3 + 60*c^5*k0^4 - (6*I)*c^4*k0^5))/(16*k0^2)}, 5, 11, 1]

besseltransforms/4-2-3

@@ -0,0 +1,2 @@
+(k^2*(-3 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 - 4*k^2*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) - 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 6*k^2*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 24*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 - 4*k^2*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) - 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + k^2*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3)/(3*k^3*k0^2)
+SeriesData[k, Infinity, {(15*c^4)/k0^2, 0, (105*c^4)/2 - (490*c^6)/k0^2 + ((315*I)*c^5)/k0, 0, -6615*c^6 + (187677*c^8)/(16*k0^2) - ((14175*I)*c^7)/k0 + (2835*I)/2*c^5*k0 + (945*c^4*k0^2)/8, 0, (-165*(49346*c^10 - (85050*I)*c^9*k0 - 62559*c^8*k0^2 + (25200*I)*c^7*k0^3 + 5880*c^6*k0^4 - (756*I)*c^5*k0^5 - 42*c^4*k0^6))/(32*k0^2)}, 4, 11, 1]

besseltransforms/4-2-4

@@ -0,0 +1,2 @@
+-((k^2*(-2 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 2*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 6*k^2*(-2 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 12*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + k^2*(-2 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 2*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4)/(k^4*k0^2))
+SeriesData[k, Infinity, {(48*c^4)/k0^2, (-315*c^5)/k0^2 + ((105*I)*c^4)/k0, 0, (-2835*c^5)/2 + (4725*c^7)/k0^2 - ((4410*I)*c^6)/k0 + (315*I)/2*c^4*k0, 0, (-693*(2025*c^9 - (2979*I)*c^8*k0 - 1800*c^7*k0^2 + (560*I)*c^6*k0^3 + 90*c^5*k0^4 - (6*I)*c^4*k0^5))/(16*k0^2)}, 4, 11, 1]

besseltransforms/4-2-5

@@ -0,0 +1,2 @@
+(-4*(k^4*(-5 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5) + 6*(k^4*(-5 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5) - 4*(k^4*(-5 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5) + k^4*(-5 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + k^4*(-5 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5)/(5*k^5*k0^2)
+SeriesData[k, Infinity, {(105*c^4)/k0^2, (-1152*c^5)/k0^2 + ((384*I)*c^4)/k0, (-945*c^4)/2 + (4410*c^6)/k0^2 - ((2835*I)*c^5)/k0, 0, 24255*c^6 - (688149*c^8)/(16*k0^2) + ((51975*I)*c^7)/k0 - (10395*I)/2*c^5*k0 - (3465*c^4*k0^2)/8, 0, (429*(49346*c^10 - (85050*I)*c^9*k0 - 62559*c^8*k0^2 + (25200*I)*c^7*k0^3 + 5880*c^6*k0^4 - (756*I)*c^5*k0^5 - 42*c^4*k0^6))/(32*k0^2)}, 4, 11, 1]

besseltransforms/4-2-6

@@ -0,0 +1,2 @@
+(-3*k^4*(-3 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 8*k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 + 12*k^4*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 32*k^2*(-3 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 - 18*k^4*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 48*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 96*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 + 12*k^4*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 32*k^2*(-3 + 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6 - 3*k^4*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 8*k^2*(3 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6)/(3*k^6*k0^2)
+SeriesData[k, Infinity, {(192*c^4)/k0^2, (-2835*c^5)/k0^2 + ((945*I)*c^4)/k0, -1920*c^4 + (17920*c^6)/k0^2 - ((11520*I)*c^5)/k0, (31185*c^5)/2 - (51975*c^7)/k0^2 + ((48510*I)*c^6)/k0 - (3465*I)/2*c^4*k0, 0, (3003*(2025*c^9 - (2979*I)*c^8*k0 - 1800*c^7*k0^2 + (560*I)*c^6*k0^3 + 90*c^5*k0^4 - (6*I)*c^4*k0^5))/(16*k0^2)}, 4, 11, 1]

besseltransforms/4-2-7

@@ -0,0 +1,2 @@
+(-4*(k^6*(-7 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7) + 6*(k^6*(-7 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7) - 4*(k^6*(-7 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7) + k^6*(-7 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7 + k^6*(-7 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7)/(7*k^7*k0^2)
+SeriesData[k, Infinity, {(315*c^4)/k0^2, (-1920*(3*c^5 - I*c^4*k0))/k0^2, (3465*(28*c^6 - (18*I)*c^5*k0 - 3*c^4*k0^2))/(2*k0^2), (-7680*(30*c^7 - (28*I)*c^6*k0 - 9*c^5*k0^2 + I*c^4*k0^3))/k0^2, (9009*(993*c^8 - (1200*I)*c^7*k0 - 560*c^6*k0^2 + (120*I)*c^5*k0^3 + 10*c^4*k0^4))/(16*k0^2), 0, (-2145*(49346*c^10 - (85050*I)*c^9*k0 - 62559*c^8*k0^2 + (25200*I)*c^7*k0^3 + 5880*c^6*k0^4 - (756*I)*c^5*k0^5 - 42*c^4*k0^6))/(32*k0^2)}, 4, 11, 1]

besseltransforms/4-3-0

@@ -0,0 +1,2 @@
+
+Simplify::time: Time spent on a transformation exceeded 300. seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification.

besseltransforms/4-3-1

@@ -0,0 +1,2 @@
+
+Simplify::time: Time spent on a transformation exceeded 300. seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification.

besseltransforms/4-3-2

@@ -0,0 +1,2 @@
+(8*k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) - 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 12*k^2*(-3 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 24*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 8*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) - 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 2*k^2*(-3 + 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 3*k^2*k0*Sqrt[Pi]*(Piecewise[{{0, k^2/k0^2 <= 1}}, (4*(k^2 - k0^2)^(3/2))/(3*k^2*k0*Sqrt[Pi])] + I*Piecewise[{{(-2*(2*k0*(k0 - Sqrt[-k^2 + k0^2]) + k^2*(-3 + (2*Sqrt[-k^2 + k0^2])/k0)))/(3*k^2*Sqrt[Pi]), k^2/k0^2 < 1}, {(2*(1 - (2*k0^2)/(3*k^2)))/Sqrt[Pi], k^2/k0^2 > 1}}, 0]))/(12*k^2*k0^3)
+SeriesData[k, Infinity, {(3*c^4)/k0^3, 0, (-5*(13*c^6 - (12*I)*c^5*k0 - 3*c^4*k0^2))/(2*k0^3), 0, (105*I)*c^5 + (5103*c^8)/(16*k0^3) - ((525*I)*c^7)/k0^2 - (1365*c^6)/(4*k0) + (105*c^4*k0)/8, 0, (-15*(6821*c^10 - (15540*I)*c^9*k0 - 15309*c^8*k0^2 + (8400*I)*c^7*k0^3 + 2730*c^6*k0^4 - (504*I)*c^5*k0^5 - 42*c^4*k0^6))/(32*k0^3)}, 3, 11, 1]

besseltransforms/4-3-3

@@ -0,0 +1,2 @@
+(k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 2*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 4*k^2*(-3 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 6*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 12*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 4*k^2*(-3 + 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 8*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + k^2*(3 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 - 2*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4)/(6*k^3*k0^3)
+SeriesData[k, Infinity, {(8*c^4)/k0^3, (-45*c^5)/k0^3 + ((15*I)*c^4)/k0^2, 0, (35*I)/2*c^4 + (525*c^7)/k0^3 - ((490*I)*c^6)/k0^2 - (315*c^5)/(2*k0), 0, (-63*(2025*c^9 - (2979*I)*c^8*k0 - 1800*c^7*k0^2 + (560*I)*c^6*k0^3 + 90*c^5*k0^4 - (6*I)*c^4*k0^5))/(16*k0^3), 0, (165*(25080*c^11 - (49346*I)*c^10*k0 - 42525*c^9*k0^2 + (20853*I)*c^8*k0^3 + 6300*c^7*k0^4 - (1176*I)*c^6*k0^5 - 126*c^5*k0^6 + (6*I)*c^4*k0^7))/(32*k0^3)}, 3, 11, 1]

besseltransforms/4-3-4

@@ -0,0 +1,2 @@
+(-4*(k^4*(-15 + 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5) + 6*(k^4*(-15 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5) - 4*(k^4*(-15 + 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5) + k^4*(-15 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + k^4*(-15 + 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5)/(60*k^4*k0^3)
+SeriesData[k, Infinity, {(15*c^4)/k0^3, (-48*(3*c^5 - I*c^4*k0))/k0^3, (35*(28*c^6 - (18*I)*c^5*k0 - 3*c^4*k0^2))/(2*k0^3), 0, (-63*(993*c^8 - (1200*I)*c^7*k0 - 560*c^6*k0^2 + (120*I)*c^5*k0^3 + 10*c^4*k0^4))/(16*k0^3), 0, (33*(49346*c^10 - (85050*I)*c^9*k0 - 62559*c^8*k0^2 + (25200*I)*c^7*k0^3 + 5880*c^6*k0^4 - (756*I)*c^5*k0^5 - 42*c^4*k0^6))/(32*k0^3)}, 3, 11, 1]

besseltransforms/4-3-5

@@ -0,0 +1,2 @@
+((5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(120*k^5) - (5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6)/(30*k^5) + (5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6)/(20*k^5) - (5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6)/(30*k^5) + (5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6)/(120*k^5))/k0^3
+SeriesData[k, Infinity, {(24*c^4)/k0^3, (-315*c^5)/k0^3 + ((105*I)*c^4)/k0^2, (1792*c^6)/k0^3 - ((1152*I)*c^5)/k0^2 - (192*c^4)/k0, (-315*I)/2*c^4 - (4725*c^7)/k0^3 + ((4410*I)*c^6)/k0^2 + (2835*c^5)/(2*k0), 0, (231*(2025*c^9 - (2979*I)*c^8*k0 - 1800*c^7*k0^2 + (560*I)*c^6*k0^3 + 90*c^5*k0^4 - (6*I)*c^4*k0^5))/(16*k0^3), 0, (-429*(25080*c^11 - (49346*I)*c^10*k0 - 42525*c^9*k0^2 + (20853*I)*c^8*k0^3 + 6300*c^7*k0^4 - (1176*I)*c^6*k0^5 - 126*c^5*k0^6 + (6*I)*c^4*k0^7))/(32*k0^3)}, 3, 11, 1]

besseltransforms/4-3-6

@@ -0,0 +1,2 @@
+((k^6*(-35 + 6*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7)/(210*k^6) - (2*(k^6*(-35 + 6*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7))/(105*k^6) + (k^6*(-35 + 6*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7)/(35*k^6) - (2*(k^6*(-35 + 6*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7))/(105*k^6) + (k^6*(-35 + 6*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7)/(210*k^6))/k0^3
+SeriesData[k, Infinity, {(35*c^4)/k0^3, (-576*c^5)/k0^3 + ((192*I)*c^4)/k0^2, (4410*c^6)/k0^3 - ((2835*I)*c^5)/k0^2 - (945*c^4)/(2*k0), (-640*I)*c^4 - (19200*c^7)/k0^3 + ((17920*I)*c^6)/k0^2 + (5760*c^5)/k0, (10395*I)/2*c^5 + (688149*c^8)/(16*k0^3) - ((51975*I)*c^7)/k0^2 - (24255*c^6)/k0 + (3465*c^4*k0)/8, 0, (-143*(49346*c^10 - (85050*I)*c^9*k0 - 62559*c^8*k0^2 + (25200*I)*c^7*k0^3 + 5880*c^6*k0^4 - (756*I)*c^5*k0^5 - 42*c^4*k0^6))/(32*k0^3)}, 3, 11, 1]

besseltransforms/4-3-7

@@ -0,0 +1,2 @@
+((7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^8)/(336*k^7) - (7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^8)/(84*k^7) + (7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^8)/(56*k^7) - (7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^8)/(84*k^7) + (7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^8)/(336*k^7))/k0^3
+SeriesData[k, Infinity, {(48*c^4)/k0^3, (-945*c^5)/k0^3 + ((315*I)*c^4)/k0^2, (8960*c^6)/k0^3 - ((5760*I)*c^5)/k0^2 - (960*c^4)/k0, (-3465*I)/2*c^4 - (51975*c^7)/k0^3 + ((48510*I)*c^6)/k0^2 + (31185*c^5)/(2*k0), (23040*I)*c^5 + (190656*c^8)/k0^3 - ((230400*I)*c^7)/k0^2 - (107520*c^6)/k0 + 1920*c^4*k0, (-3003*(2025*c^9 - (2979*I)*c^8*k0 - 1800*c^7*k0^2 + (560*I)*c^6*k0^3 + 90*c^5*k0^4 - (6*I)*c^4*k0^5))/(16*k0^3), 0, (2145*(25080*c^11 - (49346*I)*c^10*k0 - 42525*c^9*k0^2 + (20853*I)*c^8*k0^3 + 6300*c^7*k0^4 - (1176*I)*c^6*k0^5 - 126*c^5*k0^6 + (6*I)*c^4*k0^7))/(32*k0^3)}, 3, 11, 1]

besseltransforms/4-4-0

@@ -0,0 +1,9 @@
+Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^4*BesselJ[0, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 0 && q == 4 && κ == 4 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0]
+
+                              -5 c x + I k0 x        c x 4                                2  2               4  4               6  6               8  8      Pi                                                   2  2              4  4              6  6               8  8
+                             E                (-1 + E   )  ((-418854310875 + 29682132480 k  x  - 3901685760 k  x  + 1258291200 k  x  - 2147483648 k  x ) Cos[-- + k x] + 4 Sqrt[2] k x (13043905875 - 1229437440 k  x  + 240844800 k  x  - 150994944 k  x  + 2147483648 k  x ) (Cos[k x] + Sin[k x]))
+                                                                                                                                                             4
+Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}.
+                                                                                                                                                          19/2   4             25/2
+                                                                                                                                              8589934592 k     k0  Sqrt[2 Pi] x
+Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^4*BesselJ[0, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 0 && q == 4 && κ == 4 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}]

besseltransforms/4-4-1

@@ -0,0 +1,9 @@
+Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^4*BesselJ[1, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 1 && q == 4 && κ == 4 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0]
+
+                                -5 c x + I k0 x        c x 4                                    2  2              4  4              6  6               8  8      Pi                                         2  2               4  4              6  6               8  8      Pi
+                             -(E                (-1 + E   )  (8 k x (-14783093325 + 1452971520 k  x  - 309657600 k  x  + 251658240 k  x  + 2147483648 k  x ) Cos[-- + k x] - 3 (156043762875 - 11416204800 k  x  + 1589575680 k  x  - 587202560 k  x  + 2147483648 k  x ) Sin[-- + k x]))
+                                                                                                                                                                 4                                                                                                            4
+Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}.
+                                                                                                                                                    19/2   4             25/2
+                                                                                                                                        8589934592 k     k0  Sqrt[2 Pi] x
+Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^4*BesselJ[1, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 1 && q == 4 && κ == 4 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}]

besseltransforms/4-4-2

@@ -0,0 +1,9 @@
+Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^4*BesselJ[2, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 2 && q == 4 && κ == 4 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0]
+
+                                -5 c x + I k0 x        c x 4                                 2  2              4  4              6  6               8  8      Pi                                                   2  2              4  4               6  6               8  8
+                             -(E                (-1 + E   )  (15 (-43692253605 + 3528645120 k  x  - 590413824 k  x  + 352321536 k  x  + 2147483648 k  x ) Cos[-- + k x] + 4 Sqrt[2] k x (21606059475 - 2421619200 k  x  + 681246720 k  x  - 1761607680 k  x  + 2147483648 k  x ) (Cos[k x] + Sin[k x])))
+                                                                                                                                                              4
+Integrate::idiv: Integral of --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- does not converge on {0, Infinity}.
+                                                                                                                                                            19/2   4             25/2
+                                                                                                                                                8589934592 k     k0  Sqrt[2 Pi] x
+Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^4*BesselJ[2, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 2 && q == 4 && κ == 4 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}]

besseltransforms/4-4-3

@@ -0,0 +1,2 @@
+(-4*(k^4*(-15 + 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5) + 6*(k^4*(-15 + 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5) - 4*(k^4*(-15 + 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5) + k^4*(-15 + 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + k^4*(-15 + 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5)/(120*k^3*k0^4)
+SeriesData[k, Infinity, {(3*c^4)/k0^4, (-8*(3*c^5 - I*c^4*k0))/k0^4, (5*(28*c^6 - (18*I)*c^5*k0 - 3*c^4*k0^2))/(2*k0^4), 0, (-7*(993*c^8 - (1200*I)*c^7*k0 - 560*c^6*k0^2 + (120*I)*c^5*k0^3 + 10*c^4*k0^4))/(16*k0^4), 0, (3*(49346*c^10 - (85050*I)*c^9*k0 - 62559*c^8*k0^2 + (25200*I)*c^7*k0^3 + 5880*c^6*k0^4 - (756*I)*c^5*k0^5 - 42*c^4*k0^6))/(32*k0^4), 0, ((-5*(c - I*k0)^12)/128 + (5*(2*c - I*k0)^12)/32 - (15*(3*c - I*k0)^12)/64 + (5*(4*c - I*k0)^12)/32 - (5*(5*c - I*k0)^12)/128)/(120*k0^4)}, 2, 11, 1]

besseltransforms/4-4-4

@@ -0,0 +1,2 @@
+((5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(240*k^4) - (5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6)/(60*k^4) + (5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6)/(40*k^4) - (5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6)/(60*k^4) + (5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6)/(240*k^4))/k0^4
+SeriesData[k, Infinity, {(4*c^4)/k0^4, (-45*c^5)/k0^4 + ((15*I)*c^4)/k0^3, (224*c^6)/k0^4 - ((144*I)*c^5)/k0^3 - (24*c^4)/k0^2, (-35*(30*c^7 - (28*I)*c^6*k0 - 9*c^5*k0^2 + I*c^4*k0^3))/(2*k0^4), 0, (21*(2025*c^9 - (2979*I)*c^8*k0 - 1800*c^7*k0^2 + (560*I)*c^6*k0^3 + 90*c^5*k0^4 - (6*I)*c^4*k0^5))/(16*k0^4), 0, (-33*(25080*c^11 - (49346*I)*c^10*k0 - 42525*c^9*k0^2 + (20853*I)*c^8*k0^3 + 6300*c^7*k0^4 - (1176*I)*c^6*k0^5 - 126*c^5*k0^6 + (6*I)*c^4*k0^7))/(32*k0^4)}, 2, 11, 1]

besseltransforms/4-4-5

@@ -0,0 +1,2 @@
+((k^6*(-35 + 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7)/(840*k^5) - (k^6*(-35 + 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7)/(210*k^5) + (k^6*(-35 + 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7)/(140*k^5) - (k^6*(-35 + 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7)/(210*k^5) + (k^6*(-35 + 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7)/(840*k^5))/k0^4
+SeriesData[k, Infinity, {(5*c^4)/k0^4, (-72*c^5)/k0^4 + ((24*I)*c^4)/k0^3, (490*c^6)/k0^4 - ((315*I)*c^5)/k0^3 - (105*c^4)/(2*k0^2), (-1920*c^7)/k0^4 + ((1792*I)*c^6)/k0^3 + (576*c^5)/k0^2 - ((64*I)*c^4)/k0, (63*(993*c^8 - (1200*I)*c^7*k0 - 560*c^6*k0^2 + (120*I)*c^5*k0^3 + 10*c^4*k0^4))/(16*k0^4), 0, (-11*(49346*c^10 - (85050*I)*c^9*k0 - 62559*c^8*k0^2 + (25200*I)*c^7*k0^3 + 5880*c^6*k0^4 - (756*I)*c^5*k0^5 - 42*c^4*k0^6))/(32*k0^4), 0, (143*(682591*c^12 - (1504800*I)*c^11*k0 - 1480380*c^10*k0^2 + (850500*I)*c^9*k0^3 + 312795*c^8*k0^4 - (75600*I)*c^7*k0^5 - 11760*c^6*k0^6 + (1080*I)*c^5*k0^7 + 45*c^4*k0^8))/(640*k0^4)}, 2, 11, 1]

besseltransforms/4-4-6

@@ -0,0 +1,2 @@
+((35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^8)/(6720*k^6) - (35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^8)/(1680*k^6) + (35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^8)/(1120*k^6) - (35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^8)/(1680*k^6) + (35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^8)/(6720*k^6))/k0^4
+SeriesData[k, Infinity, {(6*c^4)/k0^4, (-105*c^5)/k0^4 + ((35*I)*c^4)/k0^3, (896*c^6)/k0^4 - ((576*I)*c^5)/k0^3 - (96*c^4)/k0^2, (-315*(30*c^7 - (28*I)*c^6*k0 - 9*c^5*k0^2 + I*c^4*k0^3))/(2*k0^4), 160*c^4 + (15888*c^8)/k0^4 - ((19200*I)*c^7)/k0^3 - (8960*c^6)/k0^2 + ((1920*I)*c^5)/k0, (-231*(2025*c^9 - (2979*I)*c^8*k0 - 1800*c^7*k0^2 + (560*I)*c^6*k0^3 + 90*c^5*k0^4 - (6*I)*c^4*k0^5))/(16*k0^4), 0, (143*(25080*c^11 - (49346*I)*c^10*k0 - 42525*c^9*k0^2 + (20853*I)*c^8*k0^3 + 6300*c^7*k0^4 - (1176*I)*c^6*k0^5 - 126*c^5*k0^6 + (6*I)*c^4*k0^7))/(32*k0^4)}, 2, 11, 1]

besseltransforms/4-4-7

@@ -0,0 +1,2 @@
+((k^8*(-105 + 16*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^9)/(5040*k^7) - (k^8*(-105 + 16*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^9)/(1260*k^7) + (k^8*(-105 + 16*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^9)/(840*k^7) - (k^8*(-105 + 16*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^9)/(1260*k^7) + (k^8*(-105 + 16*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^9)/(5040*k^7))/k0^4
+SeriesData[k, Infinity, {(7*c^4)/k0^4, (-48*(3*c^5 - I*c^4*k0))/k0^4, (105*(28*c^6 - (18*I)*c^5*k0 - 3*c^4*k0^2))/(2*k0^4), (-320*(30*c^7 - (28*I)*c^6*k0 - 9*c^5*k0^2 + I*c^4*k0^3))/k0^4, (693*(993*c^8 - (1200*I)*c^7*k0 - 560*c^6*k0^2 + (120*I)*c^5*k0^3 + 10*c^4*k0^4))/(16*k0^4), (-64*(2025*c^9 - (2979*I)*c^8*k0 - 1800*c^7*k0^2 + (560*I)*c^6*k0^3 + 90*c^5*k0^4 - (6*I)*c^4*k0^5))/k0^4, (143*(49346*c^10 - (85050*I)*c^9*k0 - 62559*c^8*k0^2 + (25200*I)*c^7*k0^3 + 5880*c^6*k0^4 - (756*I)*c^5*k0^5 - 42*c^4*k0^6))/(32*k0^4), 0, ((-13*(c - I*k0)^12)/3072 + (13*(2*c - I*k0)^12)/768 - (13*(3*c - I*k0)^12)/512 + (13*(4*c - I*k0)^12)/768 - (13*(5*c - I*k0)^12)/3072)/k0^4}, 2, 11, 1]

besseltransforms/5-1-0.REMOVED.git-id

@@ -0,0 +1 @@
+6b5039445ac40a8e4dde06ee71a446ec8c971871

besseltransforms/5-1-1.REMOVED.git-id

@@ -0,0 +1 @@
+f5594061661eec519d31142141692d67f7b41978

besseltransforms/5-1-2.REMOVED.git-id

@@ -0,0 +1 @@
+a1c5acb5509b38870c8f208e65cec91b86716900

besseltransforms/5-1-3

@@ -0,0 +1,2 @@
+((k^2*(-3 + Sqrt[1 + k^2/(c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2)/(k^3*Sqrt[1 + k^2/(c - I*k0)^2]) - (5*(k^2*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(2*c - I*k0)^2]) + (10*(k^2*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(3*c - I*k0)^2]) - (10*(k^2*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(4*c - I*k0)^2]) + (5*(k^2*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(5*c - I*k0)^2]) - (k^2*(-3 + Sqrt[1 + k^2/(6*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2)/(k^3*Sqrt[1 + k^2/(6*c - I*k0)^2]))/k0
+SeriesData[k, Infinity, {(-105*c^5)/(k*k0), 0, (945*(38*c^7 - (21*I)*c^6*k0 - 3*c^5*k0^2))/(2*k*k0), 0, (-17325*(1087*c^9 - (1134*I)*c^8*k0 - 456*c^7*k0^2 + (84*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k*k0)}, 5, 11, 1]

besseltransforms/5-1-4

@@ -0,0 +1,2 @@
+((k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4)/(k^4*Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) - (5*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) + (10*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)) - (10*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(4*c - I*k0)^2]*(4*c - I*k0)) + (5*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(5*c - I*k0)^2]*(5*c - I*k0)) - (k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4)/(k^4*Sqrt[1 + k^2/(6*c - I*k0)^2]*(6*c - I*k0)))/k0
+SeriesData[k, Infinity, {((-945*I)*c^5)/k + (6615*c^6)/(2*k*k0), 0, (-10395*(189*c^8 - (152*I)*c^7*k0 - 42*c^6*k0^2 + (4*I)*c^5*k0^3))/(8*k*k0), 0, (45045*(8547*c^10 - (10870*I)*c^9*k0 - 5670*c^8*k0^2 + (1520*I)*c^7*k0^3 + 210*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k*k0)}, 6, 11, 1]

besseltransforms/5-1-5

@@ -0,0 +1,2 @@
+((k^4*(-5 + Sqrt[1 + k^2/(c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4)/(k^5*Sqrt[1 + k^2/(c - I*k0)^2]) - (5*(k^4*(-5 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(2*c - I*k0)^2]) + (10*(k^4*(-5 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(3*c - I*k0)^2]) - (10*(k^4*(-5 + Sqrt[1 + k^2/(4*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(4*c - I*k0)^2]) + (5*(k^4*(-5 + Sqrt[1 + k^2/(5*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(5*c - I*k0)^2]) - (k^4*(-5 + Sqrt[1 + k^2/(6*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4)/(k^5*Sqrt[1 + k^2/(6*c - I*k0)^2]))/k0
+SeriesData[k, Infinity, {(945*c^5)/(k*k0), 0, (-3465*(38*c^7 - (21*I)*c^6*k0 - 3*c^5*k0^2))/(2*k*k0), 0, (45045*(1087*c^9 - (1134*I)*c^8*k0 - 456*c^7*k0^2 + (84*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k*k0)}, 5, 11, 1]

besseltransforms/5-1-6

@@ -0,0 +1,2 @@
+((k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(k^6*Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) - (5*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6))/(k^6*Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) + (10*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6))/(k^6*Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)) - (10*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6))/(k^6*Sqrt[1 + k^2/(4*c - I*k0)^2]*(4*c - I*k0)) + (5*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6))/(k^6*Sqrt[1 + k^2/(5*c - I*k0)^2]*(5*c - I*k0)) - (k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6)/(k^6*Sqrt[1 + k^2/(6*c - I*k0)^2]*(6*c - I*k0)))/k0
+SeriesData[k, Infinity, {(3840*c^5)/(k*k0), ((10395*I)*c^5)/k - (72765*c^6)/(2*k*k0), 0, (45045*(189*c^8 - (152*I)*c^7*k0 - 42*c^6*k0^2 + (4*I)*c^5*k0^3))/(8*k*k0), 0, (-135135*(8547*c^10 - (10870*I)*c^9*k0 - 5670*c^8*k0^2 + (1520*I)*c^7*k0^3 + 210*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k*k0)}, 5, 11, 1]

besseltransforms/5-1-7

@@ -0,0 +1,2 @@
+((k^6*(-7 + Sqrt[1 + k^2/(c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(k^7*Sqrt[1 + k^2/(c - I*k0)^2]) - (5*(k^6*(-7 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6))/(k^7*Sqrt[1 + k^2/(2*c - I*k0)^2]) + (10*(k^6*(-7 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6))/(k^7*Sqrt[1 + k^2/(3*c - I*k0)^2]) - (10*(k^6*(-7 + Sqrt[1 + k^2/(4*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6))/(k^7*Sqrt[1 + k^2/(4*c - I*k0)^2]) + (5*(k^6*(-7 + Sqrt[1 + k^2/(5*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6))/(k^7*Sqrt[1 + k^2/(5*c - I*k0)^2]) - (k^6*(-7 + Sqrt[1 + k^2/(6*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6)/(k^7*Sqrt[1 + k^2/(6*c - I*k0)^2]))/k0
+SeriesData[k, Infinity, {(10395*c^5)/(k*k0), ((46080*I)*c^5)/k - (161280*c^6)/(k*k0), (45045*(38*c^7 - (21*I)*c^6*k0 - 3*c^5*k0^2))/(2*k*k0), 0, (-225225*(1087*c^9 - (1134*I)*c^8*k0 - 456*c^7*k0^2 + (84*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k*k0)}, 5, 11, 1]

besseltransforms/5-2-0

@@ -0,0 +1,9 @@
+Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^2*x), {x, 0, Infinity}, Assumptions -> n == 0 && q == 2 && κ == 5]
+
+                                            I k0 x     Pi                         -5 c x + I k0 x     Pi                       -4 c x + I k0 x     Pi                       -3 c x + I k0 x     Pi                       -2 c x + I k0 x     Pi                       -(c x) + I k0 x     Pi                     I k0 x     Pi                      -5 c x + I k0 x     Pi                    -4 c x + I k0 x     Pi                    -3 c x + I k0 x     Pi                    -2 c x + I k0 x     Pi                    -(c x) + I k0 x     Pi                  I k0 x     Pi                   -5 c x + I k0 x     Pi                 -4 c x + I k0 x     Pi                 -3 c x + I k0 x     Pi                 -2 c x + I k0 x     Pi                 -(c x) + I k0 x     Pi               I k0 x     Pi               -5 c x + I k0 x     Pi              -4 c x + I k0 x     Pi              -3 c x + I k0 x     Pi              -2 c x + I k0 x     Pi              -(c x) + I k0 x     Pi           I k0 x      2       Pi           -5 c x + I k0 x      2       Pi             -4 c x + I k0 x      2       Pi              -3 c x + I k0 x      2       Pi              -2 c x + I k0 x      2       Pi             -(c x) + I k0 x      2       Pi                         I k0 x     Pi                          -5 c x + I k0 x     Pi                         -4 c x + I k0 x     Pi                         -3 c x + I k0 x     Pi                         -2 c x + I k0 x     Pi                         -(c x) + I k0 x     Pi                      I k0 x     Pi                       -5 c x + I k0 x     Pi                     -4 c x + I k0 x     Pi                     -3 c x + I k0 x     Pi                     -2 c x + I k0 x     Pi                     -(c x) + I k0 x     Pi                    I k0 x     Pi                    -5 c x + I k0 x     Pi                  -4 c x + I k0 x     Pi                  -3 c x + I k0 x     Pi                  -2 c x + I k0 x     Pi                  -(c x) + I k0 x     Pi                I k0 x     Pi                -5 c x + I k0 x     Pi               -4 c x + I k0 x     Pi               -3 c x + I k0 x     Pi               -2 c x + I k0 x     Pi               -(c x) + I k0 x     Pi             I k0 x     Pi              -5 c x + I k0 x     Pi             -4 c x + I k0 x     Pi             -3 c x + I k0 x     Pi             -2 c x + I k0 x     Pi             -(c x) + I k0 x     Pi
+                               13043905875 E       Cos[-- - k x]     13043905875 E                Cos[-- - k x]   65219529375 E                Cos[-- - k x]   65219529375 E                Cos[-- - k x]   65219529375 E                Cos[-- - k x]   65219529375 E                Cos[-- - k x]     2401245 E       Cos[-- - k x]      2401245 E                Cos[-- - k x]   12006225 E                Cos[-- - k x]   12006225 E                Cos[-- - k x]   12006225 E                Cos[-- - k x]   12006225 E                Cos[-- - k x]     3675 E       Cos[-- - k x]      3675 E                Cos[-- - k x]   18375 E                Cos[-- - k x]   18375 E                Cos[-- - k x]   18375 E                Cos[-- - k x]   18375 E                Cos[-- - k x]     9 E       Cos[-- - k x]     9 E                Cos[-- - k x]   45 E                Cos[-- - k x]   45 E                Cos[-- - k x]   45 E                Cos[-- - k x]   45 E                Cos[-- - k x]   E       Sqrt[--] Cos[-- - k x]   E                Sqrt[--] Cos[-- - k x]   5 E                Sqrt[--] Cos[-- - k x]   10 E                Sqrt[--] Cos[-- - k x]   10 E                Sqrt[--] Cos[-- - k x]   5 E                Sqrt[--] Cos[-- - k x]    418854310875 E       Sin[-- - k x]     418854310875 E                Sin[-- - k x]   2094271554375 E                Sin[-- - k x]   2094271554375 E                Sin[-- - k x]   2094271554375 E                Sin[-- - k x]   2094271554375 E                Sin[-- - k x]     57972915 E       Sin[-- - k x]      57972915 E                Sin[-- - k x]   289864575 E                Sin[-- - k x]   289864575 E                Sin[-- - k x]   289864575 E                Sin[-- - k x]   289864575 E                Sin[-- - k x]      59535 E       Sin[-- - k x]      59535 E                Sin[-- - k x]   297675 E                Sin[-- - k x]   297675 E                Sin[-- - k x]   297675 E                Sin[-- - k x]   297675 E                Sin[-- - k x]     75 E       Sin[-- - k x]     75 E                Sin[-- - k x]   375 E                Sin[-- - k x]   375 E                Sin[-- - k x]   375 E                Sin[-- - k x]   375 E                Sin[-- - k x]     E       Sin[-- - k x]      E                Sin[-- - k x]   5 E                Sin[-- - k x]   5 E                Sin[-- - k x]   5 E                Sin[-- - k x]   5 E                Sin[-- - k x]
+                                                       4                                              4                                            4                                            4                                            4                                            4                                 4                                           4                                         4                                         4                                         4                                         4                              4                                        4                                      4                                      4                                      4                                      4                           4                                    4                                   4                                   4                                   4                                   4                        Pi      4                                 Pi      4                                   Pi      4                                    Pi      4                                    Pi      4                                   Pi      4                                     4                                               4                                              4                                              4                                              4                                              4                                  4                                            4                                          4                                          4                                          4                                          4                                4                                         4                                       4                                       4                                       4                                       4                            4                                     4                                    4                                    4                                    4                                    4                         4                                   4                                  4                                  4                                  4                                  4
+Integrate::idiv: Integral of ------------------------------------- - ------------------------------------------ + ------------------------------------------ - ------------------------------------------ + ------------------------------------------ - ------------------------------------------ - ---------------------------------- + -------------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- + --------------------------------------- + ------------------------------- - ----------------------------------- + ------------------------------------ - ------------------------------------ + ------------------------------------ - ------------------------------------ - --------------------------- + -------------------------------- - --------------------------------- + --------------------------------- - --------------------------------- + --------------------------------- + ------------------------------ - --------------------------------------- + ----------------------------------------- - ------------------------------------------ + ------------------------------------------ - ----------------------------------------- - ------------------------------------- + ------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- + ----------------------------------- - --------------------------------------- + ---------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- - --------------------------------- + ------------------------------------ - ------------------------------------- + ------------------------------------- - ------------------------------------- + ------------------------------------- + ---------------------------- - --------------------------------- + ---------------------------------- - ---------------------------------- + ---------------------------------- - ---------------------------------- - -------------------------- + ------------------------------ - -------------------------------- + -------------------------------- - -------------------------------- + -------------------------------- does not converge on {0, Infinity}.
+                                         17/2   2             19/2                 17/2   2             19/2                    17/2   2             19/2                    17/2   2             19/2                    17/2   2             19/2                    17/2   2             19/2               13/2   2             15/2              13/2   2             15/2                13/2   2             15/2                 13/2   2             15/2                 13/2   2             15/2                 13/2   2             15/2             9/2   2             11/2            9/2   2             11/2              9/2   2             11/2               9/2   2             11/2               9/2   2             11/2               9/2   2             11/2          5/2   2             7/2         5/2   2             7/2             5/2   2             7/2             5/2   2             7/2             5/2   2             7/2             5/2   2             7/2                       2  3/2                               2  3/2                                     2  3/2                                       2  3/2                                       2  3/2                                      2  3/2                            19/2   2             21/2                  19/2   2             21/2                     19/2   2             21/2                      19/2   2             21/2                      19/2   2             21/2                      19/2   2             21/2                 15/2   2             17/2               15/2   2             17/2                 15/2   2             17/2                  15/2   2             17/2                  15/2   2             17/2                  15/2   2             17/2              11/2   2             13/2            11/2   2             13/2               11/2   2             13/2              11/2   2             13/2               11/2   2             13/2                11/2   2             13/2          7/2   2             9/2          7/2   2             9/2              7/2   2             9/2              7/2   2             9/2              7/2   2             9/2              7/2   2             9/2         3/2   2             5/2        3/2   2             5/2           3/2   2             5/2            3/2   2             5/2            3/2   2             5/2            3/2   2             5/2
+                             1073741824 k     k0  Sqrt[2 Pi] x         1073741824 k     k0  Sqrt[2 Pi] x            1073741824 k     k0  Sqrt[2 Pi] x             536870912 k     k0  Sqrt[2 Pi] x             536870912 k     k0  Sqrt[2 Pi] x            1073741824 k     k0  Sqrt[2 Pi] x          2097152 k     k0  Sqrt[2 Pi] x         2097152 k     k0  Sqrt[2 Pi] x           2097152 k     k0  Sqrt[2 Pi] x            1048576 k     k0  Sqrt[2 Pi] x            1048576 k     k0  Sqrt[2 Pi] x            2097152 k     k0  Sqrt[2 Pi] x          16384 k    k0  Sqrt[2 Pi] x         16384 k    k0  Sqrt[2 Pi] x           16384 k    k0  Sqrt[2 Pi] x             8192 k    k0  Sqrt[2 Pi] x             8192 k    k0  Sqrt[2 Pi] x            16384 k    k0  Sqrt[2 Pi] x          64 k    k0  Sqrt[2 Pi] x        64 k    k0  Sqrt[2 Pi] x            64 k    k0  Sqrt[2 Pi] x            32 k    k0  Sqrt[2 Pi] x            32 k    k0  Sqrt[2 Pi] x            64 k    k0  Sqrt[2 Pi] x                Sqrt[k] k0  x                        Sqrt[k] k0  x                              Sqrt[k] k0  x                                Sqrt[k] k0  x                                Sqrt[k] k0  x                               Sqrt[k] k0  x                   8589934592 k     k0  Sqrt[2 Pi] x          8589934592 k     k0  Sqrt[2 Pi] x             8589934592 k     k0  Sqrt[2 Pi] x              4294967296 k     k0  Sqrt[2 Pi] x              4294967296 k     k0  Sqrt[2 Pi] x              8589934592 k     k0  Sqrt[2 Pi] x           16777216 k     k0  Sqrt[2 Pi] x         16777216 k     k0  Sqrt[2 Pi] x           16777216 k     k0  Sqrt[2 Pi] x             8388608 k     k0  Sqrt[2 Pi] x             8388608 k     k0  Sqrt[2 Pi] x            16777216 k     k0  Sqrt[2 Pi] x          131072 k     k0  Sqrt[2 Pi] x        131072 k     k0  Sqrt[2 Pi] x           131072 k     k0  Sqrt[2 Pi] x           65536 k     k0  Sqrt[2 Pi] x            65536 k     k0  Sqrt[2 Pi] x            131072 k     k0  Sqrt[2 Pi] x         512 k    k0  Sqrt[2 Pi] x        512 k    k0  Sqrt[2 Pi] x            512 k    k0  Sqrt[2 Pi] x            256 k    k0  Sqrt[2 Pi] x            256 k    k0  Sqrt[2 Pi] x            512 k    k0  Sqrt[2 Pi] x         4 k    k0  Sqrt[2 Pi] x        4 k    k0  Sqrt[2 Pi] x           4 k    k0  Sqrt[2 Pi] x            2 k    k0  Sqrt[2 Pi] x            2 k    k0  Sqrt[2 Pi] x            4 k    k0  Sqrt[2 Pi] x
+Series[Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^2*x), {x, 0, Infinity}, Assumptions -> n == 0 && q == 2 && κ == 5], {k, Infinity, 10}]

besseltransforms/5-2-1

@@ -0,0 +1,2 @@
+(-10*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 20*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) - 20*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 10*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) - 2*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + k*Sqrt[Pi]*(Piecewise[{{0, k^2/k0^2 <= 1}}, (2*Sqrt[k^2 - k0^2])/(k*Sqrt[Pi])] + I*Piecewise[{{(2*k0)/(k*Sqrt[Pi]), k0^2/k^2 < 1}, {(2*(k0 - Sqrt[-k^2 + k0^2]))/(k*Sqrt[Pi]), k0^2/k^2 > 1}}, 0]))/(2*k*k0^2)
+Piecewise[{{SeriesData[k, Infinity, {(-225*c^6)/(2*k0^2) + ((45*I)*c^5)/k0, 0, (-7875*c^6)/4 + (39375*c^8)/(8*k0^2) - ((5250*I)*c^7)/k0 + (525*I)/2*c^5*k0, 0, (-2205*(2025*c^10 - (3310*I)*c^9*k0 - 2250*c^8*k0^2 + (800*I)*c^7*k0^3 + 150*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^2)}, 6, 11, 1], (k0 <= 0 && k^2/k0^2 > 1) || k0 > 0}}, SeriesData[k, Infinity, {-k0^(-2), 0, 1/2, 0, ((5*c*(c - I*k0)^3)/8 - (5*c*(2*c - I*k0)^3)/2 + (15*c*(3*c - I*k0)^3)/4 - (5*c*(4*c - I*k0)^3)/2 + (5*c*(5*c - I*k0)^3)/8 - (5*I)/8*(c - I*k0)^3*k0 + (5*I)/4*(2*c - I*k0)^3*k0 - (5*I)/4*(3*c - I*k0)^3*k0 + (5*I)/8*(4*c - I*k0)^3*k0 - I/8*(5*c - I*k0)^3*k0)/k0^2, 0, ((-5*c*(c - I*k0)^5)/16 + (5*c*(2*c - I*k0)^5)/4 - (15*c*(3*c - I*k0)^5)/8 + (5*c*(4*c - I*k0)^5)/4 - (5*c*(5*c - I*k0)^5)/16 + (5*I)/16*(c - I*k0)^5*k0 - (5*I)/8*(2*c - I*k0)^5*k0 + (5*I)/8*(3*c - I*k0)^5*k0 - (5*I)/16*(4*c - I*k0)^5*k0 + I/16*(5*c - I*k0)^5*k0)/k0^2, 0, ((25*c*(c - I*k0)^7)/128 - (25*c*(2*c - I*k0)^7)/32 + (75*c*(3*c - I*k0)^7)/64 - (25*c*(4*c - I*k0)^7)/32 + (25*c*(5*c - I*k0)^7)/128 - (25*I)/128*(c - I*k0)^7*k0 + (25*I)/64*(2*c - I*k0)^7*k0 - (25*I)/64*(3*c - I*k0)^7*k0 + (25*I)/128*(4*c - I*k0)^7*k0 - (5*I)/128*(5*c - I*k0)^7*k0)/k0^2, 0, ((-35*c*(c - I*k0)^9)/256 + (35*c*(2*c - I*k0)^9)/64 - (105*c*(3*c - I*k0)^9)/128 + (35*c*(4*c - I*k0)^9)/64 - (35*c*(5*c - I*k0)^9)/256 + (35*I)/256*(c - I*k0)^9*k0 - (35*I)/128*(2*c - I*k0)^9*k0 + (35*I)/128*(3*c - I*k0)^9*k0 - (35*I)/256*(4*c - I*k0)^9*k0 + (7*I)/256*(5*c - I*k0)^9*k0)/k0^2}, 0, 11, 1]]

besseltransforms/5-2-2

@@ -0,0 +1,2 @@
+(-k^2 + 10*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 20*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 20*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 10*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 2*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + k^2*Sqrt[Pi]*(I*Piecewise[{{0, k^2/k0^2 <= 1}}, (2*k0*Sqrt[k^2 - k0^2])/(k^2*Sqrt[Pi])] + Piecewise[{{(k^2 + 2*k0*(-k0 + Sqrt[-k^2 + k0^2]))/(k^2*Sqrt[Pi]), k^2/k0^2 < 1}, {(1 - (2*k0^2)/k^2)/Sqrt[Pi], k^2/k0^2 > 1}}, 0]))/(2*k^2*k0^2)
+SeriesData[k, Infinity, {(-15*c^5)/k0^2, 0, (-315*c^5)/2 + (1050*c^7)/k0^2 - ((1575*I)/2*c^6)/k0, 0, (-1575*(331*c^9 - (450*I)*c^8*k0 - 240*c^7*k0^2 + (60*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k0^2)}, 5, 11, 1]

besseltransforms/5-2-3

@@ -0,0 +1,2 @@
+(k^2*(-3 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 - 5*k^2*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) - 20*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 10*k^2*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 40*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 - 10*k^2*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) - 40*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 5*k^2*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 20*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 - k^2*(-3 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) - 4*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3)/(3*k^3*k0^2)
+SeriesData[k, Infinity, {(735*c^6)/(2*k0^2) - ((105*I)*c^5)/k0, 0, (19845*c^6)/4 - (178605*c^8)/(8*k0^2) + ((17955*I)*c^7)/k0 - (945*I)/2*c^5*k0, 0, (3465*(8547*c^10 - (10870*I)*c^9*k0 - 5670*c^8*k0^2 + (1520*I)*c^7*k0^3 + 210*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^2)}, 6, 11, 1]

besseltransforms/5-2-4

@@ -0,0 +1,2 @@
+(-(k^2*(-2 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2) - 2*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 5*k^2*(-2 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 10*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 10*k^2*(-2 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 20*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 10*k^2*(-2 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 20*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 5*k^2*(-2 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 - 10*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + k^2*(-2 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 2*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4)/(k^4*k0^2)
+SeriesData[k, Infinity, {(105*c^5)/k0^2, 0, (945*c^5)/2 - (5985*c^7)/k0^2 + ((6615*I)/2*c^6)/k0, 0, (3465*(1087*c^9 - (1134*I)*c^8*k0 - 456*c^7*k0^2 + (84*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k0^2)}, 5, 11, 1]

besseltransforms/5-2-5

@@ -0,0 +1,2 @@
+((k^4*(-5 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5)/(5*k^5) - (k^4*(-5 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5)/k^5 + (2*(k^4*(-5 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5))/k^5 - (2*(k^4*(-5 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5))/k^5 + (k^4*(-5 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5)/k^5 - (k^4*(-5 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5)/(5*k^5))/k0^2
+SeriesData[k, Infinity, {(384*c^5)/k0^2, (-6615*c^6)/(2*k0^2) + ((945*I)*c^5)/k0, 0, (-72765*c^6)/4 + (654885*c^8)/(8*k0^2) - ((65835*I)*c^7)/k0 + (3465*I)/2*c^5*k0, 0, (-9009*(8547*c^10 - (10870*I)*c^9*k0 - 5670*c^8*k0^2 + (1520*I)*c^7*k0^3 + 210*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^2)}, 5, 11, 1]

besseltransforms/5-2-6

@@ -0,0 +1,2 @@
+((k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(6*k^6) - (5*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6))/(6*k^6) + (5*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6))/(3*k^6) - (5*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6))/(3*k^6) + (5*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6))/(6*k^6) - (k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6)/(6*k^6))/k0^2
+SeriesData[k, Infinity, {(945*c^5)/k0^2, (-13440*c^6)/k0^2 + ((3840*I)*c^5)/k0, (-10395*c^5)/2 + (65835*c^7)/k0^2 - ((72765*I)/2*c^6)/k0, 0, (-15015*(1087*c^9 - (1134*I)*c^8*k0 - 456*c^7*k0^2 + (84*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k0^2)}, 5, 11, 1]

besseltransforms/5-2-7

@@ -0,0 +1,2 @@
+((k^6*(-7 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7)/(7*k^7) - (5*(k^6*(-7 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7))/(7*k^7) + (10*(k^6*(-7 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7))/(7*k^7) - (10*(k^6*(-7 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7))/(7*k^7) + (5*(k^6*(-7 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7))/(7*k^7) - (k^6*(-7 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^7)/(7*k^7))/k0^2
+SeriesData[k, Infinity, {(1920*c^5)/k0^2, (-72765*c^6)/(2*k0^2) + ((10395*I)*c^5)/k0, -23040*c^5 + (291840*c^7)/k0^2 - ((161280*I)*c^6)/k0, (945945*c^6)/4 - (8513505*c^8)/(8*k0^2) + ((855855*I)*c^7)/k0 - (45045*I)/2*c^5*k0, 0, (45045*(8547*c^10 - (10870*I)*c^9*k0 - 5670*c^8*k0^2 + (1520*I)*c^7*k0^3 + 210*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^2)}, 5, 11, 1]

besseltransforms/5-3-0

@@ -0,0 +1,2 @@
+
+Simplify::time: Time spent on a transformation exceeded 300. seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification.

besseltransforms/5-3-1

@@ -0,0 +1,2 @@
+
+Simplify::time: Time spent on a transformation exceeded 300. seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification.

besseltransforms/5-3-2

@@ -0,0 +1,2 @@
+(10*k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) - 20*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 20*k^2*(-3 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 40*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 20*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) - 40*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 10*k^2*(-3 + 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 20*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 2*k^2*(3 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) - 4*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 3*k^2*k0*Sqrt[Pi]*(Piecewise[{{0, k^2/k0^2 <= 1}}, (4*(k^2 - k0^2)^(3/2))/(3*k^2*k0*Sqrt[Pi])] + I*Piecewise[{{(-2*(2*k0*(k0 - Sqrt[-k^2 + k0^2]) + k^2*(-3 + (2*Sqrt[-k^2 + k0^2])/k0)))/(3*k^2*Sqrt[Pi]), k^2/k0^2 < 1}, {(2*(1 - (2*k0^2)/(3*k^2)))/Sqrt[Pi], k^2/k0^2 > 1}}, 0]))/(12*k^2*k0^3)
+SeriesData[k, Infinity, {(75*c^6)/(2*k0^3) - ((15*I)*c^5)/k0^2, 0, (-105*(75*c^8 - (80*I)*c^7*k0 - 30*c^6*k0^2 + (4*I)*c^5*k0^3))/(8*k0^3), 0, (315*(2025*c^10 - (3310*I)*c^9*k0 - 2250*c^8*k0^2 + (800*I)*c^7*k0^3 + 150*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^3)}, 5, 11, 1]