DLMF:10.22.E13 (Q3387)

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DLMF:10.22.E13
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    test
    ∫ 0 1 2 ⁢ π J 2 ⁢ ν ⁡ ( 2 ⁢ z ⁢ cos ⁡ θ ) ⁢ cos ⁡ ( 2 ⁢ μ ⁢ θ ) ⁢ d θ = 1 2 ⁢ π ⁢ J ν + μ ⁡ ( z ) ⁢ J ν - μ ⁡ ( z ) , superscript subscript 0 1 2 𝜋 Bessel-J 2 𝜈 2 𝑧 𝜃 2 𝜇 𝜃 𝜃 1 2 𝜋 Bessel-J 𝜈 𝜇 𝑧 Bessel-J 𝜈 𝜇 𝑧 {\displaystyle{\displaystyle\int_{0}^{\frac{1}{2}\pi}J_{2\nu}\left(2z\cos% \theta\right)\cos\left(2\mu\theta\right)\mathrm{d}\theta=\tfrac{1}{2}\pi J_{% \nu+\mu}\left(z\right)J_{\nu-\mu}\left(z\right),}}
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    DLMF id
    DLMF:10.22.E13
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