DLMF:18.12.E5 (Q5647)

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DLMF:18.12.E5
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    Statements

    Defining formula
    1 - x ⁢ z ( 1 - 2 ⁢ x ⁢ z + z 2 ) λ + 1 = ∑ n = 0 ∞ n + 2 ⁢ λ 2 ⁢ λ ⁢ C n ( λ ) ⁡ ( x ) ⁢ z n , 1 𝑥 𝑧 superscript 1 2 𝑥 𝑧 superscript 𝑧 2 𝜆 1 superscript subscript 𝑛 0 𝑛 2 𝜆 2 𝜆 ultraspherical-Gegenbauer-polynomial 𝜆 𝑛 𝑥 superscript 𝑧 𝑛 {\displaystyle{\displaystyle\frac{1-xz}{(1-2xz+z^{2})^{\lambda+1}}=\sum_{n=0}^% {\infty}\frac{n+2\lambda}{2\lambda}C^{(\lambda)}_{n}\left(x\right)z^{n},}}
    0 references
    DLMF id
    DLMF:18.12.E5
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    constraint
    | z | < 1 𝑧 1 {\displaystyle{\displaystyle|z|<1}}
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    Symbols used
    Q11475
    Defining formula
    C n ( λ ) ⁡ ( x ) ultraspherical-Gegenbauer-polynomial 𝜆 𝑛 𝑥 {\displaystyle{\displaystyle C^{(\NVar{\lambda})}_{\NVar{n}}\left(\NVar{x}% \right)}}
    xml-id
    C18.S3.T1.t1.r3.m2aadec
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    Q11750
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C18.S1.XMD2.m1ddec
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    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1ddec
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    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1ddec
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