DLMF:10.22.E14 (Q3388)

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DLMF:10.22.E14
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    Statements

    test
    ∫ 0 π J 2 ⁢ ν ⁡ ( 2 ⁢ z ⁢ sin ⁡ θ ) ⁢ cos ⁡ ( 2 ⁢ μ ⁢ θ ) ⁢ d θ = π ⁢ cos ⁡ ( 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)% \cos\left(2\mu\theta\right)\mathrm{d}\theta=\pi\cos\left(\mu\pi\right)J_{\nu+% \mu}\left(z\right)J_{\nu-\mu}\left(z\right),}}
    0 references
    DLMF id
    DLMF:10.22.E14
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    constraint
    ℜ ⁡ ν > - 1 2 𝜈 1 2 {\displaystyle{\displaystyle\Re\nu>-\tfrac{1}{2}}}
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    Symbols used
    Bessel function of the first kind
    test
    J ν ⁡ ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E2.m2afdec
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    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
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    cosine function
    test
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2aadec
    0 references
     
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