DLMF:2.8.E36 (Q972)

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DLMF:2.8.E36
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    Statements

    Defining formula
    W n , 4 ⁢ ( u , ξ ) = | ξ | 1 / 2 ⁢ Y ν ⁡ ( u ⁢ | ξ | 1 / 2 ) ⁢ ∑ s = 0 n - 1 A s ⁢ ( ξ ) u 2 ⁢ s - | ξ | ⁢ Y ν + 1 ⁡ ( u ⁢ | ξ | 1 / 2 ) ⁢ ∑ s = 0 n - 2 B s ⁢ ( ξ ) u 2 ⁢ s + 1 + | ξ | 1 / 2 ⁢ env ⁢ Y ν ⁡ ( u ⁢ | ξ | 1 / 2 ) ⁢ O ⁡ ( 1 u 2 ⁢ n - 1 ) , subscript 𝑊 𝑛 4 𝑢 𝜉 superscript 𝜉 1 2 Bessel-Y-Weber 𝜈 𝑢 superscript 𝜉 1 2 superscript subscript 𝑠 0 𝑛 1 subscript 𝐴 𝑠 𝜉 superscript 𝑢 2 𝑠 𝜉 Bessel-Y-Weber 𝜈 1 𝑢 superscript 𝜉 1 2 superscript subscript 𝑠 0 𝑛 2 subscript 𝐵 𝑠 𝜉 superscript 𝑢 2 𝑠 1 superscript 𝜉 1 2 envelope-Bessel-Y 𝜈 𝑢 superscript 𝜉 1 2 Big-O 1 superscript 𝑢 2 𝑛 1 {\displaystyle{\displaystyle W_{n,4}(u,\xi)=|\xi|^{1/2}Y_{\nu}\left(u|\xi|^{1/% 2}\right)\sum_{s=0}^{n-1}\frac{A_{s}(\xi)}{u^{2s}}-|\xi|Y_{\nu+1}\left(u|\xi|^% {1/2}\right)\sum_{s=0}^{n-2}\frac{B_{s}(\xi)}{u^{2s+1}}+|\xi|^{1/2}\mathrm{env% }\mskip-2.0mu Y_{\nu}\left(u|\xi|^{1/2}\right)O\left(\frac{1}{u^{2n-1}}\right)% ,}}
    0 references
    DLMF id
    DLMF:2.8.E36
    0 references
    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
    0 references
    order not exceeding
    Defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2akdec
    0 references
    Q11091
    Defining formula
    env ⁢ Y ν ⁡ ( x ) envelope-Bessel-Y 𝜈 𝑥 {\displaystyle{\displaystyle\mathrm{env}\mskip-2.0mu Y_{\NVar{\nu}}\left(\NVar% {x}\right)}}
    xml-id
    C2.S8.SS4.p5.m4abdec
    0 references
    Q11085
    Defining formula
    W n , j ⁢ ( u , ξ ) subscript 𝑊 𝑛 𝑗 𝑢 𝜉 {\displaystyle{\displaystyle W_{n,j}(u,\xi)}}
    xml-id
    C2.S8.XMD20.m1fdec
    0 references
    Q11086
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C2.S8.XMD21.m1ldec
    0 references
    Q11087
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C2.S8.XMD22.m1edec
    0 references
    Q11088
    Defining formula
    A s ⁢ ( ξ ) subscript 𝐴 𝑠 𝜉 {\displaystyle{\displaystyle A_{s}(\xi)}}
    xml-id
    C2.S8.XMD23.m1hdec
    0 references
    Q11089
    Defining formula
    B s ⁢ ( ξ ) subscript 𝐵 𝑠 𝜉 {\displaystyle{\displaystyle B_{s}(\xi)}}
    xml-id
    C2.S8.XMD24.m1hdec
    0 references
    Q11069
    Defining formula
    u 𝑢 {\displaystyle{\displaystyle u}}
    xml-id
    C2.S8.XMD4.m1rdec
    0 references
     
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