DLMF:10.22.E51 (Q3425)

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DLMF:10.22.E51
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    test
    ∫ 0 ∞ J ν ⁡ ( b ⁢ t ) ⁢ exp ⁡ ( - p 2 ⁢ t 2 ) ⁢ t ν + 1 ⁢ d t = b ν ( 2 ⁢ p 2 ) ν + 1 ⁢ exp ⁡ ( - b 2 4 ⁢ p 2 ) , superscript subscript 0 Bessel-J 𝜈 𝑏 𝑡 superscript 𝑝 2 superscript 𝑡 2 superscript 𝑡 𝜈 1 𝑡 superscript 𝑏 𝜈 superscript 2 superscript 𝑝 2 𝜈 1 superscript 𝑏 2 4 superscript 𝑝 2 {\displaystyle{\displaystyle\int_{0}^{\infty}J_{\nu}\left(bt\right)\exp\left(-% p^{2}t^{2}\right)t^{\nu+1}\mathrm{d}t=\frac{b^{\nu}}{(2p^{2})^{\nu+1}}\exp% \left(-\frac{b^{2}}{4p^{2}}\right),}}
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    DLMF:10.22.E51
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