DLMF:10.22.E56 (Q3430): Difference between revisions

Revision as of 13:23, 2 January 2020

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Language	Label	Description	Also known as
English	DLMF:10.22.E56	No description defined

{\displaystyle{\displaystyle\int_{0}^{\infty}\frac{J_{\mu}\left(at\right)J_{% \nu}\left(bt\right)}{t^{\lambda}}\mathrm{d}t=\frac{a^{\mu}\Gamma\left(\frac{1}% {2}\nu+\frac{1}{2}\mu-\frac{1}{2}\lambda+\frac{1}{2}\right)}{2^{\lambda}b^{\mu% -\lambda+1}\Gamma\left(\frac{1}{2}\nu-\frac{1}{2}\mu+\frac{1}{2}\lambda+\frac{% 1}{2}\right)}\*\mathbf{F}\left(\tfrac{1}{2}(\mu+\nu-\lambda+1),\tfrac{1}{2}(% \mu-\nu-\lambda+1);\mu+1;\frac{a^{2}}{b^{2}}\right),}}

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DLMF:10.22.E56

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{\displaystyle{\displaystyle\Re(\mu+\nu+1)>\Re\lambda>-1}}

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{\displaystyle{\displaystyle 0<a<b}}

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{\displaystyle{\displaystyle\Re(\mu+\nu+1)>\Re\lambda>-1}}

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{\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}

C10.S2.E2.m2aapdec

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

C5.S2.E1.m2aqdec

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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.m2aqdec