DLMF:10.43.E24 (Q3638): Difference between revisions

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ν > - 1 𝜈 1 {\displaystyle{\displaystyle\Re\nu>-1}}

\realpart@@{\nu}>-1
Property / constraint: ν > - 1 𝜈 1 {\displaystyle{\displaystyle\Re\nu>-1}} / rank
 
Normal rank

Revision as of 17:40, 30 December 2019

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DLMF:10.43.E24
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    Statements

    0 I ν ( b t ) exp ( - p 2 t 2 ) d t = π 2 p exp ( b 2 8 p 2 ) I 1 2 ν ( b 2 8 p 2 ) , superscript subscript 0 modified-Bessel-first-kind 𝜈 𝑏 𝑡 superscript 𝑝 2 superscript 𝑡 2 𝑡 𝜋 2 𝑝 superscript 𝑏 2 8 superscript 𝑝 2 modified-Bessel-first-kind 1 2 𝜈 superscript 𝑏 2 8 superscript 𝑝 2 {\displaystyle{\displaystyle\int_{0}^{\infty}I_{\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)I_{\frac{1}{2}\nu}\left(\frac{b^{2}}{8p^{2}}\right),}}
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    DLMF:10.43.E24
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    ν > - 1 𝜈 1 {\displaystyle{\displaystyle\Re\nu>-1}}
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