DLMF:10.22.E15 (Q3389)

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DLMF:10.22.E15
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    Defining formula
    ∫ 0 π J 2 ⁢ ν ⁡ ( 2 ⁢ z ⁢ sin ⁡ θ ) ⁢ sin ⁡ ( 2 ⁢ μ ⁢ θ ) ⁢ d θ = π ⁢ sin ⁡ ( μ ⁢ π ) ⁢ J ν + μ ⁡ ( z ) ⁢ J ν - μ ⁡ ( z ) , superscript subscript 0 𝜋 Bessel-J 2 𝜈 2 𝑧 𝜃 2 𝜇 𝜃 𝜃 𝜋 𝜇 𝜋 Bessel-J 𝜈 𝜇 𝑧 Bessel-J 𝜈 𝜇 𝑧 {\displaystyle{\displaystyle\int_{0}^{\pi}J_{2\nu}\left(2z\sin\theta\right)% \sin\left(2\mu\theta\right)\mathrm{d}\theta=\pi\sin\left(\mu\pi\right)J_{\nu+% \mu}\left(z\right)J_{\nu-\mu}\left(z\right),}}
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    DLMF id
    DLMF:10.22.E15
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