DLMF:13.16.E7 (Q4558): Difference between revisions

Revision as of 16:11, 2 January 2020

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Language	Label	Description	Also known as
English	DLMF:13.16.E7	No description defined

{\displaystyle{\displaystyle W_{\kappa,\mu}\left(z\right)=\frac{(-1)^{n}e^{-% \frac{1}{2}z}z^{\frac{1}{2}-\mu-n}}{\Gamma\left(1+2\mu\right)\Gamma\left(\frac% {1}{2}-\mu-\kappa\right)}\*\int_{0}^{\infty}\frac{M_{-\kappa,\mu}\left(t\right% )e^{-\frac{1}{2}t}t^{n+\mu-\frac{1}{2}}}{t+z}\mathrm{d}t,}}

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DLMF:13.16.E7

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{\displaystyle{\displaystyle|\operatorname{ph}z|<\pi}}

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{\displaystyle{\displaystyle-\Re(1+2\mu)<n<\left|\Re\mu\right|+\Re\kappa<% \tfrac{1}{2}}}

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{\displaystyle{\displaystyle|\operatorname{ph}z|<\pi}}

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{\displaystyle{\displaystyle n=0,1,2,\dots}}

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{\displaystyle{\displaystyle-\Re(1+2\mu)<n<\left|\Re\mu\right|+\Re\kappa<% \tfrac{1}{2}}}

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{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

C5.S2.E1.m2afdec

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@@ Property / Symbols used @@
+gamma function
@@ Property / Symbols used: gamma function / rank @@
+Normal rank
@@ Property / Symbols used: gamma function / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$ 
\EulerGamma@{\NVar{z}}
@@ Property / Symbols used: gamma function / qualifier @@
+xml-id: C5.S2.E1.m2afdec