DLMF:10.43.E22 (Q3636): Difference between revisions
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imported>Admin Admin moved page Main Page to Verifying DLMF with Maple and Mathematica |
imported>Admin Admin moved page Main Page to Verifying DLMF with Maple and Mathematica |
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| Property / Symbols used | |||
| Property / Symbols used: Q11481 / rank | |||
Normal rank | |||
| Property / Symbols used: Q11481 / qualifier | |||
test: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \assLegendreP[\NVar{\mu}]{\NVar{\nu}}@{\NVar{z}}}\assLegendreP[\NVar{\mu}]{\NVar{\nu}}@{\NVar{z}} | |||
| Property / Symbols used: Q11481 / qualifier | |||
xml-id: C14.S21.SS1.p1.m1adec | |||
Revision as of 13:02, 2 January 2020
No description defined
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | DLMF:10.43.E22 |
No description defined |
Statements
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}t^{\mu-1}e^{-at}\modBesselK{\nu}@{t}\diff{t}=\begin{cases}\left(\frac{1}{2}\pi\right)^{\frac{1}{2}}\EulerGamma@{\mu-\nu}\EulerGamma@{\mu+\nu}(1-a^{2})^{-\frac{1}{2}\mu+\frac{1}{4}}\FerrersP[-\mu+\frac{1}{2}]{\nu-\frac{1}{2}}@{a},&-1<a<1,\\ \left(\frac{1}{2}\pi\right)^{\frac{1}{2}}\EulerGamma@{\mu-\nu}\EulerGamma@{\mu+\nu}(a^{2}-1)^{-\frac{1}{2}\mu+\frac{1}{4}}\assLegendreP[-\mu+\frac{1}{2}]{\nu-\frac{1}{2}}@{a},&\realpart@@{a}\geq 0,a\neq 1.\end{cases}}
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