DLMF:10.7.E4 (Q3057)

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DLMF:10.7.E4
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    Statements

    Defining formula
    Y ν ⁡ ( z ) ∼ - ( 1 / π ) ⁢ Γ ⁡ ( ν ) ⁢ ( 1 2 ⁢ z ) - ν , asymptotically-equals Bessel-Y-Weber 𝜈 𝑧 1 𝜋 Euler-Gamma 𝜈 superscript 1 2 𝑧 𝜈 {\displaystyle{\displaystyle Y_{\nu}\left(z\right)\sim-(1/\pi)\Gamma\left(\nu% \right)(\tfrac{1}{2}z)^{-\nu},}}
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    DLMF id
    DLMF:10.7.E4
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    constraint
    ℜ ⁡ ν > 0 𝜈 0 {\displaystyle{\displaystyle\Re\nu>0}}
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    ℜ ⁡ ν > 0 𝜈 0 {\displaystyle{\displaystyle\Re\nu>0}}
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    ν = - 1 2 , - 3 2 , - 5 2 , … 𝜈 1 2 3 2 5 2 … {\displaystyle{\displaystyle\nu=-\tfrac{1}{2},-\tfrac{3}{2},-\tfrac{5}{2},% \ldots}}
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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.m2aadec
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    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2aadec
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    asymptotic equality
    Defining formula
    ∼ asymptotically-equals {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.E1.m2acdec
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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.m2abdec
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