DLMF:10.22.E18 (Q3392)

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DLMF:10.22.E18
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    Statements

    test
    ∫ 0 1 2 ⁢ π Y 0 ⁡ ( 2 ⁢ z ⁢ sin ⁡ θ ) ⁢ cos ⁡ ( 2 ⁢ n ⁢ θ ) ⁢ d θ = 1 2 ⁢ π ⁢ J n ⁡ ( z ) ⁢ Y n ⁡ ( z ) , superscript subscript 0 1 2 𝜋 Bessel-Y-Weber 0 2 𝑧 𝜃 2 𝑛 𝜃 𝜃 1 2 𝜋 Bessel-J 𝑛 𝑧 Bessel-Y-Weber 𝑛 𝑧 {\displaystyle{\displaystyle\int_{0}^{\frac{1}{2}\pi}Y_{0}\left(2z\sin\theta% \right)\cos\left(2n\theta\right)\mathrm{d}\theta=\tfrac{1}{2}\pi J_{n}\left(z% \right)Y_{n}\left(z\right),}}
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    DLMF id
    DLMF:10.22.E18
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    constraint
    n = 0 , 1 , 2 , … 𝑛 0 1 2 … {\displaystyle{\displaystyle n=0,1,2,\dots}}
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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.m2ajdec
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    Bessel function of the second kind
    test
    Y ν ⁡ ( z ) Bessel-Y-Weber 𝜈 𝑧 {\displaystyle{\displaystyle Y_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E3.m2aadec
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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.m2afdec
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    cosine function
    test
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2addec
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    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aqdec
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