DLMF:10.22.E52 (Q3426)

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DLMF:10.22.E52
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    0 J ν ( b t ) exp ( - p 2 t 2 ) d t = π 2 p exp ( - b 2 8 p 2 ) I ν / 2 ( b 2 8 p 2 ) , superscript subscript 0 Bessel-J 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 2 superscript 𝑏 2 8 superscript 𝑝 2 {\displaystyle{\displaystyle\int_{0}^{\infty}J_{\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_{\ifrac{\nu}{2}}\left(\frac{b^{2}}{8p^{2}}\right),}}
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