DLMF:10.22.E68 (Q3442): Difference between revisions

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Property / constraint
 

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

\realpart@@{(p^{2})}>0
Property / constraint: ( p 2 ) > 0 superscript 𝑝 2 0 {\displaystyle{\displaystyle\Re(p^{2})>0}} / rank
 
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Revision as of 16:20, 30 December 2019

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DLMF:10.22.E68
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    Statements

    0 t exp ( - p 2 t 2 ) J 0 ( a t ) Y 0 ( a t ) d t = - 1 2 π p 2 exp ( - a 2 2 p 2 ) K 0 ( a 2 2 p 2 ) , superscript subscript 0 𝑡 superscript 𝑝 2 superscript 𝑡 2 Bessel-J 0 𝑎 𝑡 Bessel-Y-Weber 0 𝑎 𝑡 𝑡 1 2 𝜋 superscript 𝑝 2 superscript 𝑎 2 2 superscript 𝑝 2 modified-Bessel-second-kind 0 superscript 𝑎 2 2 superscript 𝑝 2 {\displaystyle{\displaystyle\int_{0}^{\infty}t\exp\left(-p^{2}t^{2}\right)J_{0% }\left(at\right)Y_{0}\left(at\right)\mathrm{d}t=-\frac{1}{2\pi p^{2}}\exp\left% (-\frac{a^{2}}{2p^{2}}\right)K_{0}\left(\frac{a^{2}}{2p^{2}}\right),}}
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    ( p 2 ) > 0 superscript 𝑝 2 0 {\displaystyle{\displaystyle\Re(p^{2})>0}}
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