DLMF:10.43.E27 (Q3641)

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DLMF:10.43.E27
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    test
    ∫ 0 ∞ t μ + ν + 1 ⁢ K μ ⁡ ( a ⁢ t ) ⁢ J ν ⁡ ( b ⁢ t ) ⁢ d t = ( 2 ⁢ a ) μ ⁢ ( 2 ⁢ b ) ν ⁢ Γ ⁡ ( μ + ν + 1 ) ( a 2 + b 2 ) μ + ν + 1 , superscript subscript 0 superscript 𝑡 𝜇 𝜈 1 modified-Bessel-second-kind 𝜇 𝑎 𝑡 Bessel-J 𝜈 𝑏 𝑡 𝑡 superscript 2 𝑎 𝜇 superscript 2 𝑏 𝜈 Euler-Gamma 𝜇 𝜈 1 superscript superscript 𝑎 2 superscript 𝑏 2 𝜇 𝜈 1 {\displaystyle{\displaystyle\int_{0}^{\infty}t^{\mu+\nu+1}K_{\mu}\left(at% \right)J_{\nu}\left(bt\right)\mathrm{d}t=\frac{(2a)^{\mu}(2b)^{\nu}\Gamma\left% (\mu+\nu+1\right)}{(a^{2}+b^{2})^{\mu+\nu+1}},}}
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    DLMF id
    DLMF:10.43.E27
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