DLMF:10.22.E53 (Q3427): 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.E53	No description defined

{\displaystyle{\displaystyle\int_{0}^{\infty}Y_{2\nu}\left(bt\right)\exp\left(% -p^{2}t^{2}\right)\mathrm{d}t=-\frac{\sqrt{\pi}}{2p}\exp\left(-\frac{b^{2}}{8p% ^{2}}\right)\left(I_{\nu}\left(\frac{b^{2}}{8p^{2}}\right)\tan\left(\nu\pi% \right)+\frac{1}{\pi}K_{\nu}\left(\frac{b^{2}}{8p^{2}}\right)\sec\left(\nu\pi% \right)\right),}}

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DLMF:10.22.E53

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{\displaystyle{\displaystyle|\Re\nu|<\tfrac{1}{2}}}

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{\displaystyle{\displaystyle\Re(p^{2})>0}}

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

C10.S2.E3.m2ahdec

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@@ Property / Symbols used @@
+Bessel function of the second kind
@@ Property / Symbols used: Bessel function of the second kind / rank @@
+Normal rank
@@ Property / Symbols used: Bessel function of the second kind / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle Y_{\NVar{\nu}}\left(\NVar{z}\right)}}$ 
\BesselY{\NVar{\nu}}@{\NVar{z}}
@@ Property / Symbols used: Bessel function of the second kind / qualifier @@
+xml-id: C10.S2.E3.m2ahdec