[ewald] jdu domů

Former-commit-id: 297d041a358960dba00ff03a264b5032e0419c84
This commit is contained in:
Marek Nečada 2017-09-15 22:07:06 +03:00
parent 20b24aa43c
commit 8b92c1df1d
3 changed files with 521 additions and 89 deletions

View File

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Cell[45534, 1320, 6000, 162, 347, "Input", "ExpressionUUID" -> \
"5e62d660-2944-47ca-8ee0-e6a553ed7d63"],
Cell[CellGroupData[{
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Cell[51559, 1486, 354, 7, 34, "Input", "ExpressionUUID" -> \
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}, Open ]],
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Cell[52227, 1504, 5350, 141, 259, "Input", "ExpressionUUID" -> \
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Cell[CellGroupData[{
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}, Open ]],
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Cell[58149, 1666, 5096, 134, 258, "Input", "ExpressionUUID" -> \
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Cell[CellGroupData[{
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}, Open ]],
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Cell[63792, 1821, 5074, 130, 236, "Input", "ExpressionUUID" -> \
"811cd081-362a-41a3-bd5d-f77c96ca788c"],
Cell[CellGroupData[{
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Cell[68891, 1955, 254, 6, 34, "Input", "ExpressionUUID" -> \
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Cell[69434, 1972, 4740, 127, 236, "Input", "ExpressionUUID" -> \
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Cell[CellGroupData[{
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Cell[74199, 2103, 283, 6, 34, "Input", "ExpressionUUID" -> \
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}, Open ]],
Cell[CellGroupData[{
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Cell[74890, 2123, 768, 23, 34, "Input", "ExpressionUUID" -> \
"c015003f-0699-49e2-b866-714eb92d5c6f"],
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Cell[75661, 2148, 311, 10, 63, "Output", "ExpressionUUID" -> \
"b5efa070-aee7-4251-898d-4ad75f8ee655"]
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Cell[CellGroupData[{
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Cell[76009, 2163, 211, 5, 32, "Input", "ExpressionUUID" -> \
"65bc3149-1111-4cfb-a506-bc566f00020a"],
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Cell[76223, 2170, 147, 4, 35, "Output", "ExpressionUUID" -> \
"385fc41d-508e-4bcc-87ce-366fda2afa16"]
}, Open ]],
Cell[CellGroupData[{
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Cell[76407, 2179, 380, 10, 34, "Input", "ExpressionUUID" -> \
"fbdde755-24a3-46b6-b157-f28e6b6a8022"],
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"f3bbc0c5-f6fc-4fd8-ade3-1015c944f07e"]
}, Open ]],
Cell[81184, 2284, 3362, 93, 191, "Input", "ExpressionUUID" -> \
Cell[81206, 2284, 3362, 93, 191, "Input", "ExpressionUUID" -> \
"e139a925-f883-4746-b86a-c2602253404c"],
Cell[CellGroupData[{
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Cell[84593, 2381, 336, 7, 34, "Input", "ExpressionUUID" -> \
"7c490700-b77f-4e41-bc26-5314e7de681a"],
Cell[84910, 2390, 345, 8, 34, "Output", "ExpressionUUID" -> \
Cell[84932, 2390, 345, 8, 34, "Output", "ExpressionUUID" -> \
"2ec8c9bc-264b-4c99-966f-0e16399c5a47"]
}, Open ]],
Cell[85270, 2401, 3279, 88, 191, "Input", "ExpressionUUID" -> \
Cell[85292, 2401, 3279, 88, 191, "Input", "ExpressionUUID" -> \
"03b0ced6-4edd-459d-b511-4346ebf0b6b3"],
Cell[CellGroupData[{
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Cell[88596, 2493, 334, 7, 34, "Input", "ExpressionUUID" -> \
"56fbb4e1-8f74-4c7e-a055-064f55e0a5e4"],
Cell[88911, 2502, 419, 9, 34, "Output", "ExpressionUUID" -> \
Cell[88933, 2502, 419, 9, 34, "Output", "ExpressionUUID" -> \
"ccc74805-25fc-4b7a-92ea-ecc47f1289c3"]
}, Open ]],
Cell[89345, 2514, 1338, 41, 79, "Input", "ExpressionUUID" -> \
Cell[89367, 2514, 1338, 41, 79, "Input", "ExpressionUUID" -> \
"fdc5165f-652c-4553-b7d6-e673dd5aaf0c"],
Cell[CellGroupData[{
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Cell[90730, 2559, 259, 5, 34, "Input", "ExpressionUUID" -> \
"14bbf919-b4de-4582-b295-f820ec4e1863"],
Cell[90970, 2566, 233, 5, 34, "Output", "ExpressionUUID" -> \
Cell[90992, 2566, 233, 5, 34, "Output", "ExpressionUUID" -> \
"6f771c74-3b2b-4814-8148-354f0c429799"]
}, Open ]],
Cell[91218, 2574, 2075, 58, 34, "Input", "ExpressionUUID" -> \
Cell[91240, 2574, 2075, 58, 103, "Input", "ExpressionUUID" -> \
"4fe8906e-3924-4127-922e-cba66e63b281"],
Cell[CellGroupData[{
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Cell[93340, 2636, 283, 6, 34, "Input", "ExpressionUUID" -> \
"314b1bc8-d2f0-41e7-a76a-821f0a313b1d"],
Cell[93604, 2644, 394, 8, 34, "Output", "ExpressionUUID" -> \
Cell[93626, 2644, 394, 8, 34, "Output", "ExpressionUUID" -> \
"a7a1768d-8381-468e-9182-cad6264fbeb4"]
}, Open ]],
Cell[94013, 2655, 1830, 55, 34, "Input", "ExpressionUUID" -> \
Cell[94035, 2655, 1830, 55, 103, "Input", "ExpressionUUID" -> \
"1b478334-5bf6-4ef1-a489-1d672116aa7a"],
Cell[CellGroupData[{
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Cell[95890, 2714, 230, 5, 34, "Input", "ExpressionUUID" -> \
"e3c36c04-d161-4900-98a4-33e7dc51e872"],
Cell[96101, 2721, 248, 6, 34, "Output", "ExpressionUUID" -> \
Cell[96123, 2721, 248, 6, 34, "Output", "ExpressionUUID" -> \
"fed7bff7-9bbc-40e2-8c1c-b16c41ea5128"]
}, Open ]],
Cell[96364, 2730, 1826, 53, 34, "Input", "ExpressionUUID" -> \
Cell[96386, 2730, 1826, 53, 103, "Input", "ExpressionUUID" -> \
"5d9b2d82-846d-4549-b840-40cefa18d8c0"],
Cell[CellGroupData[{
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Cell[98237, 2787, 305, 6, 34, "Input", "ExpressionUUID" -> \
"d9d5283f-d204-4f19-83d0-7773fcf3cd30"],
Cell[98523, 2795, 298, 7, 34, "Output", "ExpressionUUID" -> \
Cell[98545, 2795, 298, 7, 34, "Output", "ExpressionUUID" -> \
"09894aad-397c-465b-b0aa-c9f601a9aec6"]
}, Open ]],
Cell[98836, 2805, 1048, 28, 34, "Input", "ExpressionUUID" -> \
Cell[98858, 2805, 1048, 28, 57, "Input", "ExpressionUUID" -> \
"8d01b7f4-1b47-4870-bd56-c3d01a3b65f0"],
Cell[CellGroupData[{
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Cell[99931, 2837, 379, 7, 34, "Input", "ExpressionUUID" -> \
"ef81724d-7599-4fc6-bc9f-faa6548f8c62"],
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Cell[100313, 2846, 348, 8, 34, "Output", "ExpressionUUID" -> \
"97867d61-9c01-430e-8d6c-36bed05cf8e4"]
}, Open ]],
Cell[CellGroupData[{
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Cell[100698, 2859, 797, 27, 34, "Input", "ExpressionUUID" -> \
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Cell[101498, 2888, 186, 5, 32, "Output", "ExpressionUUID" -> \
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}, Open ]],
Cell[CellGroupData[{
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Cell[101721, 2898, 795, 26, 34, "Input", "ExpressionUUID" -> \
"ebafb28b-1247-44b5-b0f7-b0ceb9aa700d"],
Cell[102447, 2925, 212, 5, 32, "Output", "ExpressionUUID" -> \
Cell[102519, 2926, 212, 5, 32, "Output", "ExpressionUUID" -> \
"be3bbbd4-9c45-4351-a1ef-63e78194d774"]
}, Open ]],
Cell[CellGroupData[{
Cell[102768, 2936, 257, 5, 34, "Input", "ExpressionUUID" -> \
"6ed44f78-9dea-4e9b-9c6f-054174e7e82b"],
Cell[103028, 2943, 294, 5, 32, "Output", "ExpressionUUID" -> \
"7b8e4d31-ecf7-4029-83ce-7d91df23700d"]
}, Open ]],
Cell[103337, 2951, 1016, 31, 57, "Input", "ExpressionUUID" -> \
"c67c7bd2-b642-48af-8f40-996a591698e8"],
Cell[CellGroupData[{
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Cell[104636, 2994, 248, 5, 32, "Output", "ExpressionUUID" -> \
"88930c3e-c93e-4369-838f-286f7ce31f12"]
}, Open ]],
Cell[104899, 3002, 188, 3, 32, "Input", "ExpressionUUID" -> \
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Cell[105090, 3007, 3046, 91, 171, "Input", "ExpressionUUID" -> \
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Cell[CellGroupData[{
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}, Open ]],
Cell[CellGroupData[{
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"33105fcb-ed74-4431-9f6c-898062630460"]
}, Open ]],
Cell[109436, 3140, 2464, 73, 125, "Input", "ExpressionUUID" -> \
"f9b1d3e1-f9e3-47df-b296-06925e64f0cf"],
Cell[CellGroupData[{
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"ecbc543a-2554-49e6-9782-90f2af4e63f3"]
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Cell[CellGroupData[{
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"fe23d9f8-5eb2-48dd-9916-622dd20f3cdb"]
}, Open ]]
}
]

View File

@ -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

View File

@ -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