DLMF:10.17.E10 (Q3179)

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DLMF:10.17.E10
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    Y ν ( z ) ( 2 π z ) 1 2 ( cos ω k = 0 ( - 1 ) k b 2 k ( ν ) z 2 k - sin ω k = 0 ( - 1 ) k b 2 k + 1 ( ν ) z 2 k + 1 ) , asymptotic-expansion diffop Bessel-Y-Weber 𝜈 1 𝑧 superscript 2 𝜋 𝑧 1 2 𝜔 superscript subscript 𝑘 0 superscript 1 𝑘 subscript 𝑏 2 𝑘 𝜈 superscript 𝑧 2 𝑘 𝜔 superscript subscript 𝑘 0 superscript 1 𝑘 subscript 𝑏 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(\cos\omega\sum_{k=0}^{\infty}(-1)^{k}\frac{b_{2k}(% \nu)}{z^{2k}}-\sin\omega\sum_{k=0}^{\infty}(-1)^{k}\frac{b_{2k+1}(\nu)}{z^{2k+% 1}}\right),}}
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    DLMF:10.17.E10
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    | ph z | π - δ phase 𝑧 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\pi-\delta}}
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    Y ν ( z ) Bessel-Y-Weber 𝜈 𝑧 {\displaystyle{\displaystyle Y_{\NVar{\nu}}\left(\NVar{z}\right)}}
    C10.S2.E3.m2aadec
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    asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    C2.S1.SS3.p1.m11aedec
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2afdec
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    cos z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    C4.S14.E2.m2acdec
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    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    C1.S9.E7.m1afdec
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    sin z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    C4.S14.E1.m2acdec
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    k 𝑘 {\displaystyle{\displaystyle k}}
    C10.S1.XMD3.m1gdec
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    z 𝑧 {\displaystyle{\displaystyle z}}
    C10.S1.XMD6.m1gdec
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    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    C10.S1.XMD7.m1hdec
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    δ 𝛿 {\displaystyle{\displaystyle\delta}}
    C10.S1.XMD8.m1edec
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