DLMF:10.43.E29 (Q3643): Difference between revisions

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Property / constraint
 

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

\realpart@{p^{2}}>0
Property / constraint: ( p 2 ) > 0 superscript 𝑝 2 0 {\displaystyle{\displaystyle\Re\left(p^{2}\right)>0}} / rank
 
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Revision as of 17:40, 30 December 2019

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DLMF:10.43.E29
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    0 t exp ( - p 2 t 2 ) I 0 ( a t ) K 0 ( a t ) d t = 1 4 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 modified-Bessel-first-kind 0 𝑎 𝑡 modified-Bessel-second-kind 0 𝑎 𝑡 𝑡 1 4 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)I_{0% }\left(at\right)K_{0}\left(at\right)\mathrm{d}t=\frac{1}{4p^{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\left(p^{2}\right)>0}}
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