DLMF:10.22.E42 (Q3416)

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DLMF:10.22.E42
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    Statements

    Defining formula
    ∫ 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),}}
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    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
    Defining formula
    Y ν ⁡ ( z ) Bessel-Y-Weber 𝜈 𝑧 {\displaystyle{\displaystyle Y_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E3.m2addec
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    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2apdec
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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aaodec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aaodec
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    Q10811
    Defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1awdec
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    tangent function
    Defining formula
    tan ⁡ z 𝑧 {\displaystyle{\displaystyle\tan\NVar{z}}}
    xml-id
    C4.S14.E4.m2aadec
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    Q11427
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1abdec
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