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DLMF:10.20.E12 - MaRDI portal

DLMF:10.20.E12 (Q3959)

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DLMF:10.20.E12
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    Statements

    DLMF defining formula
    C k ⁢ ( ζ ) = - ζ 1 2 ⁢ ∑ j = 0 2 ⁢ k + 1 ( 3 2 ) j ⁢ v j ⁢ ζ - 3 ⁢ j / 2 ⁢ V 2 ⁢ k - j + 1 ⁢ ( ( 1 - z 2 ) - 1 2 ) , subscript 𝐶 𝑘 𝜁 superscript 𝜁 1 2 superscript subscript 𝑗 0 2 𝑘 1 superscript 3 2 𝑗 subscript 𝑣 𝑗 superscript 𝜁 3 𝑗 2 subscript 𝑉 2 𝑘 𝑗 1 superscript 1 superscript 𝑧 2 1 2 {\displaystyle{\displaystyle C_{k}(\zeta)=-\zeta^{\frac{1}{2}}\sum_{j=0}^{2k+1% }(\tfrac{3}{2})^{j}v_{j}\zeta^{-3j/2}V_{2k-j+1}\left((1-z^{2})^{-\frac{1}{2}}% \right),}}
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    comment
    Warning: Falling back to standard tex;
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    Symbols used
    nonnegative integer
    DLMF defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C10.S1.XMD3.m1hdec
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    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1kdec
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    solution
    DLMF defining formula
    ζ ⁢ ( z ) 𝜁 𝑧 {\displaystyle{\displaystyle\zeta(z)}}
    xml-id
    C10.S20.XMD1.m1kdec
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    constants
    DLMF defining formula
    v k subscript 𝑣 𝑘 {\displaystyle{\displaystyle v_{k}}}
    xml-id
    C10.S20.XMD3.m1adec
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    polynomial coefficient
    DLMF defining formula
    V k ⁢ ( p ) subscript 𝑉 𝑘 𝑝 {\displaystyle{\displaystyle V_{k}(p)}}
    xml-id
    C10.S41.XMD4.m1dec
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    Identifiers

     
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