DLMF:10.17.E4 (Q3173)

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DLMF:10.17.E4
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    Statements

    Defining formula
    Y ν ⁡ ( z ) ∼ ( 2 π ⁢ z ) 1 2 ⁢ ( sin ⁡ ω ⁢ ∑ k = 0 ∞ ( - 1 ) k ⁢ a 2 ⁢ k ⁢ ( ν ) z 2 ⁢ k + cos ⁡ ω ⁢ ∑ k = 0 ∞ ( - 1 ) k ⁢ a 2 ⁢ k + 1 ⁢ ( ν ) z 2 ⁢ k + 1 ) , asymptotic-expansion Bessel-Y-Weber 𝜈 𝑧 superscript 2 𝜋 𝑧 1 2 𝜔 superscript subscript 𝑘 0 superscript 1 𝑘 subscript 𝑎 2 𝑘 𝜈 superscript 𝑧 2 𝑘 𝜔 superscript subscript 𝑘 0 superscript 1 𝑘 subscript 𝑎 2 𝑘 1 𝜈 superscript 𝑧 2 𝑘 1 {\displaystyle{\displaystyle Y_{\nu}\left(z\right)\sim\left(\frac{2}{\pi z}% \right)^{\frac{1}{2}}\*\left(\sin\omega\sum_{k=0}^{\infty}(-1)^{k}\frac{a_{2k}% (\nu)}{z^{2k}}+\cos\omega\sum_{k=0}^{\infty}(-1)^{k}\frac{a_{2k+1}(\nu)}{z^{2k% +1}}\right),}}
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    DLMF id
    DLMF:10.17.E4
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    constraint
    | ph ⁡ z | ≤ π - δ phase 𝑧 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\pi-\delta}}
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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.m2adec
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    Q10931
    Defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11aadec
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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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    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2aadec
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    Q10817
    Defining formula
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1aadec
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    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2aadec
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