DLMF:10.22.E42 (Q3416)

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DLMF:10.22.E42
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    Statements

    test
    ∫ 0 ∞ Y ν ⁡ ( t ) ⁢ d t = - tan ⁡ ( 1 2 ⁢ ν ⁢ π ) , superscript subscript 0 Bessel-Y-Weber 𝜈 𝑡 𝑡 1 2 𝜈 𝜋 {\displaystyle{\displaystyle\int_{0}^{\infty}Y_{\nu}\left(t\right)\mathrm{d}t=% -\tan\left(\tfrac{1}{2}\nu\pi\right),}}
    0 references
    DLMF id
    DLMF:10.22.E42
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    constraint
    | ℜ ⁡ ν | < 1 𝜈 1 {\displaystyle{\displaystyle|\Re\nu|<1}}
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    Symbols used
    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.m2addec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2apdec
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