DLMF:10.8.E3 (Q3065)

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DLMF:10.8.E3
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    J ν ⁡ ( z ) ⁢ J μ ⁡ ( z ) = ( 1 2 ⁢ z ) ν + μ ⁢ ∑ k = 0 ∞ ( ν + μ + k + 1 ) k ⁢ ( - 1 4 ⁢ z 2 ) k k ! ⁢ Γ ⁡ ( ν + k + 1 ) ⁢ Γ ⁡ ( μ + k + 1 ) . Bessel-J 𝜈 𝑧 Bessel-J 𝜇 𝑧 superscript 1 2 𝑧 𝜈 𝜇 superscript subscript 𝑘 0 subscript 𝜈 𝜇 𝑘 1 𝑘 superscript 1 4 superscript 𝑧 2 𝑘 𝑘 Euler-Gamma 𝜈 𝑘 1 Euler-Gamma 𝜇 𝑘 1 {\displaystyle{\displaystyle J_{\nu}\left(z\right)J_{\mu}\left(z\right)=(% \tfrac{1}{2}z)^{\nu+\mu}\sum_{k=0}^{\infty}\frac{(\nu+\mu+k+1)_{k}(-\tfrac{1}{% 4}z^{2})^{k}}{k!\Gamma\left(\nu+k+1\right)\Gamma\left(\mu+k+1\right)}.}}
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    DLMF id
    DLMF:10.8.E3
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