DLMF:9.7.E21 (Q2830)

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DLMF:9.7.E21
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    Statements

    Defining formula
    S n ⁢ ( z ) = ( - 1 ) n - 1 ⁢ ∑ k = 0 m - 1 ( - 1 ) k ⁢ v k ⁢ G n - k ⁡ ( 2 ⁢ ζ ) ζ k + S m , n ⁢ ( z ) , subscript 𝑆 𝑛 𝑧 superscript 1 𝑛 1 superscript subscript 𝑘 0 𝑚 1 superscript 1 𝑘 subscript 𝑣 𝑘 rescaled-terminant-function 𝑛 𝑘 2 𝜁 superscript 𝜁 𝑘 subscript 𝑆 𝑚 𝑛 𝑧 {\displaystyle{\displaystyle S_{n}(z)=(-1)^{n-1}\sum_{k=0}^{m-1}(-1)^{k}v_{k}% \frac{G_{n-k}\left(2\zeta\right)}{\zeta^{k}}+S_{m,n}(z),}}
    0 references
    DLMF id
    DLMF:9.7.E21
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    Symbols used
    rescaled terminant function
    Defining formula
    G p ⁡ ( z ) rescaled-terminant-function 𝑝 𝑧 {\displaystyle{\displaystyle G_{\NVar{p}}\left(\NVar{z}\right)}}
    xml-id
    C9.S7.E22.m2aadec
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    Q11385
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C9.S1.XMD1.m1ndec
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    Q11381
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C9.S1.XMD3.m1odec
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    change of variable (locally)
    Defining formula
    ζ 𝜁 {\displaystyle{\displaystyle\zeta}}
    xml-id
    C9.S7.XMD1.m1odec
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    Q11392
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C9.S7.XMD10.m1adec
    0 references
     
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