DLMF:10.22.E26 (Q3400)

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DLMF:10.22.E26
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    0 1 2 π J μ ( z sin θ ) J ν ( ζ cos θ ) ( sin θ ) μ + 1 ( cos θ ) ν + 1 d θ = z μ ζ ν J μ + ν + 1 ( ζ 2 + z 2 ) ( ζ 2 + z 2 ) 1 2 ( μ + ν + 1 ) , superscript subscript 0 1 2 𝜋 Bessel-J 𝜇 𝑧 𝜃 Bessel-J 𝜈 𝜁 𝜃 superscript 𝜃 𝜇 1 superscript 𝜃 𝜈 1 𝜃 superscript 𝑧 𝜇 superscript 𝜁 𝜈 Bessel-J 𝜇 𝜈 1 superscript 𝜁 2 superscript 𝑧 2 superscript superscript 𝜁 2 superscript 𝑧 2 1 2 𝜇 𝜈 1 {\displaystyle{\displaystyle\int_{0}^{\frac{1}{2}\pi}J_{\mu}\left(z\sin\theta% \right)J_{\nu}\left(\zeta\cos\theta\right)(\sin\theta)^{\mu+1}(\cos\theta)^{% \nu+1}\mathrm{d}\theta=\frac{z^{\mu}\zeta^{\nu}J_{\mu+\nu+1}\left(\sqrt{\zeta^% {2}+z^{2}}\right)}{(\zeta^{2}+z^{2})^{\frac{1}{2}(\mu+\nu+1)}},}}
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    DLMF:10.22.E26
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    μ > - 1 , ν > - 1 formulae-sequence 𝜇 1 𝜈 1 {\displaystyle{\displaystyle\Re\mu>-1,\Re\nu>-1}}
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