From 8b92c1df1de70d3d72735fcfe62e58198d4afd7d Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Marek=20Ne=C4=8Dada?= Date: Fri, 15 Sep 2017 22:07:06 +0300 Subject: [PATCH] =?UTF-8?q?[ewald]=20jdu=20dom=C5=AF?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Former-commit-id: 297d041a358960dba00ff03a264b5032e0419c84 --- notes/BesselTFnumtests.nb | 539 +++++++++++++++++++++++++----- notes/ewald-calculations-apr1.lyx | 8 +- notes/ewald-calculations.lyx | 63 ++++ 3 files changed, 521 insertions(+), 89 deletions(-) diff --git a/notes/BesselTFnumtests.nb b/notes/BesselTFnumtests.nb index f9b5ea8..1480ee9 100644 --- a/notes/BesselTFnumtests.nb +++ b/notes/BesselTFnumtests.nb @@ -10,10 +10,10 @@ NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 111859, 3158] -NotebookOptionsPosition[ 102675, 2933] -NotebookOutlinePosition[ 103042, 2949] -CellTagsIndexPosition[ 102999, 2946] +NotebookDataLength[ 124133, 3523] 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770f59f..6a0a217 100644 --- a/notes/ewald-calculations-apr1.lyx +++ b/notes/ewald-calculations-apr1.lyx @@ -364,8 +364,12 @@ Again we use so \begin_inset Formula \begin{eqnarray*} -\pht n{s_{q,k_{0}}^{\textup{L}\kappa,c}}\left(k\right) & = & \koru{\frac{2^{1-q+n}}{\sqrt{\pi}}}\sum_{\sigma=0}^{\kappa}\left(-1\right)^{\sigma}\binom{\kappa}{\sigma}\frac{k^{n}}{2^{n}k_{0}^{q}\left(\sigma c-ik_{0}\right)^{2-q+n}}\sum_{s=0}^{\infty}\frac{\koru{\text{Γ}\left(\frac{2-q+n}{2}+s\right)\text{Γ}\left(\frac{3-q+n}{2}+s\right)}}{\text{Γ}(1+n+s)s!}\left(\frac{-k^{2}}{\left(\sigma c-ik_{0}\right)^{2}}\right)^{s}\\ - & = & \frac{2^{1-q+n}}{\sqrt{\pi}}\sum_{\sigma=0}^{\kappa}\left(-1\right)^{\sigma}\binom{\kappa}{\sigma}\frac{k^{n}}{2^{n}k_{0}^{q}\left(\sigma c-ik_{0}\right)^{2-q+n}}\sum_{s=0}^{\infty}\frac{\text{Γ}\left(\frac{2-q+n}{2}+s\right)\text{Γ}\left(\frac{3-q+n}{2}+s\right)}{\text{Γ}(1+n+s)s!}\left(\frac{-k^{2}}{\left(\sigma c-ik_{0}\right)^{2}}\right)^{s} +\pht n{s_{q,k_{0}}^{\textup{L}\kappa,c}}\left(k\right) & = & \koru{\frac{2^{1-q\kor{+n}}}{\sqrt{\pi}}}\sum_{\sigma=0}^{\kappa}\left(-1\right)^{\sigma}\binom{\kappa}{\sigma}\frac{k^{n}}{\kor{2^{n}}k_{0}^{q}\left(\sigma c-ik_{0}\right)^{2-q+n}}\sum_{s=0}^{\infty}\frac{\koru{\text{Γ}\left(\frac{2-q+n}{2}+s\right)\text{Γ}\left(\frac{3-q+n}{2}+s\right)}}{\text{Γ}(1+n+s)s!}\left(\frac{-k^{2}}{\left(\sigma c-ik_{0}\right)^{2}}\right)^{s}\\ +\mbox{OKShort} & = & \frac{2^{1-q}}{\sqrt{\pi}}\sum_{\sigma=0}^{\kappa}\left(-1\right)^{\sigma}\binom{\kappa}{\sigma}\frac{k^{n}}{k_{0}^{q}\left(\sigma c-ik_{0}\right)^{2-q+n}}\kor{\sum_{s=0}^{\infty}\frac{\text{Γ}\left(\frac{2-q+n}{2}+s\right)\text{Γ}\left(\frac{3-q+n}{2}+s\right)}{\text{Γ}(1+n+s)s!}\left(\frac{-k^{2}}{\left(\sigma c-ik_{0}\right)^{2}}\right)^{s}}\\ +\mbox{(D15.2.1)} & = & \frac{2^{1-q}}{\sqrt{\pi}}\sum_{\sigma=0}^{\kappa}\left(-1\right)^{\sigma}\binom{\kappa}{\sigma}\frac{k^{n}}{k_{0}^{q}\left(\sigma c-ik_{0}\right)^{2-q+n}}\koru{\frac{\text{Γ}\left(1+n\right)}{\text{Γ}\left(\frac{2-q+n}{2}\right)\text{Γ}\left(\frac{3-q+n}{2}\right)}\kor{\hgf\left(\begin{array}{c} +\frac{2-q+n}{2},\frac{3-q+n}{2}\\ +1+n +\end{array};\frac{-k^{2}}{\left(\sigma c-ik_{0}\right)^{2}}\right)}} \end{eqnarray*} \end_inset diff --git a/notes/ewald-calculations.lyx b/notes/ewald-calculations.lyx index 21c1612..28b5df6 100644 --- a/notes/ewald-calculations.lyx +++ b/notes/ewald-calculations.lyx @@ -726,6 +726,69 @@ What does this mean w.r.t. \end_inset +\end_layout + +\begin_layout Subparagraph* + +\lang english +Trash +\end_layout + +\begin_layout Standard + +\lang english +\begin_inset Note Note +status open + +\begin_layout Plain Layout + +\lang english +Now if +\begin_inset Formula $\frac{2-q+n}{2}$ +\end_inset + + or +\begin_inset Formula $\frac{3-q+n}{2}$ +\end_inset + + is non-positive integer, (D15.2.4) is applicable and the result is simply + a polynomial +\begin_inset Formula +\[ +\pht n{s_{q,k_{0}}^{\textup{L}\kappa,c}}\left(k\right)=\frac{2^{1-q}}{\sqrt{\pi}}\sum_{\sigma=0}^{\kappa}\left(-1\right)^{\sigma}\binom{\kappa}{\sigma}\frac{k^{n}}{k_{0}^{q}\left(\sigma c-ik_{0}\right)^{2-q+n}}\frac{\text{Γ}\left(1+n\right)}{\text{Γ}\left(\frac{2-q+n}{2}\right)\text{Γ}\left(\frac{3-q+n}{2}\right)}\koru{\sum_{s=0}^{\frac{q-2-n}{2}}\left(-1\right)^{s}\binom{\frac{2-q+n}{2}}{s}\frac{\left(\frac{3-q+n}{2}\right)_{s}}{\left(n+1\right)_{s}}\left(\frac{-k^{2}}{\left(\sigma c-ik_{0}\right)^{2}}\right)^{s}} +\] + +\end_inset + +if +\begin_inset Formula $-\frac{2-q+n}{2}\in\nats_{0}$ +\end_inset + + and +\begin_inset Formula +\[ +\pht n{s_{q,k_{0}}^{\textup{L}\kappa,c}}\left(k\right)=\frac{2^{1-q}}{\sqrt{\pi}}\sum_{\sigma=0}^{\kappa}\left(-1\right)^{\sigma}\binom{\kappa}{\sigma}\frac{k^{n}}{k_{0}^{q}\left(\sigma c-ik_{0}\right)^{2-q+n}}\frac{\text{Γ}\left(1+n\right)}{\text{Γ}\left(\frac{2-q+n}{2}\right)\text{Γ}\left(\frac{3-q+n}{2}\right)}\koru{\sum_{s=0}^{\frac{q-3-n}{2}}\left(-1\right)^{s}\binom{\frac{3-q+n}{2}}{s}\frac{\left(\frac{2-q+n}{2}\right)_{s}}{\left(n+1\right)_{s}}\left(\frac{-k^{2}}{\left(\sigma c-ik_{0}\right)^{2}}\right)^{s}} +\] + +\end_inset + +if +\begin_inset Formula $-\frac{3-q+n}{2}\in\nats_{0}$ +\end_inset + +. +\end_layout + +\begin_layout Plain Layout + +\lang english +This is some kind of shit, as it returns zeroes. + Where is the mistake? +\end_layout + +\end_inset + + \end_layout \end_body