DLMF:10.22.E53 (Q3427): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
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
 
Normal rank

Revision as of 17:20, 30 December 2019

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DLMF:10.22.E53
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    Statements

    0 Y 2 ν ( b t ) exp ( - p 2 t 2 ) d t = - π 2 p exp ( - b 2 8 p 2 ) ( I ν ( b 2 8 p 2 ) tan ( ν π ) + 1 π K ν ( b 2 8 p 2 ) sec ( ν π ) ) , superscript subscript 0 Bessel-Y-Weber 2 𝜈 𝑏 𝑡 superscript 𝑝 2 superscript 𝑡 2 𝑡 𝜋 2 𝑝 superscript 𝑏 2 8 superscript 𝑝 2 modified-Bessel-first-kind 𝜈 superscript 𝑏 2 8 superscript 𝑝 2 𝜈 𝜋 1 𝜋 modified-Bessel-second-kind 𝜈 superscript 𝑏 2 8 superscript 𝑝 2 𝜈 𝜋 {\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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    | ν | < 1 2 𝜈 1 2 {\displaystyle{\displaystyle|\Re\nu|<\tfrac{1}{2}}}
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    ( p 2 ) > 0 superscript 𝑝 2 0 {\displaystyle{\displaystyle\Re(p^{2})>0}}
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