DLMF:18.12.E4 (Q5646)

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DLMF:18.12.E4
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    Statements

    test
    ( 1 - 2 ⁢ x ⁢ z + z 2 ) - λ = ∑ n = 0 ∞ C n ( λ ) ⁡ ( x ) ⁢ z n = ∑ n = 0 ∞ ( 2 ⁢ λ ) n ( λ + 1 2 ) n ⁢ P n ( λ - 1 2 , λ - 1 2 ) ⁡ ( x ) ⁢ z n , superscript 1 2 𝑥 𝑧 superscript 𝑧 2 𝜆 superscript subscript 𝑛 0 ultraspherical-Gegenbauer-polynomial 𝜆 𝑛 𝑥 superscript 𝑧 𝑛 superscript subscript 𝑛 0 Pochhammer 2 𝜆 𝑛 Pochhammer 𝜆 1 2 𝑛 Jacobi-polynomial-P 𝜆 1 2 𝜆 1 2 𝑛 𝑥 superscript 𝑧 𝑛 {\displaystyle{\displaystyle(1-2xz+z^{2})^{-\lambda}=\sum_{n=0}^{\infty}C^{(% \lambda)}_{n}\left(x\right)z^{n}=\sum_{n=0}^{\infty}\frac{{\left(2\lambda% \right)_{n}}}{{\left(\lambda+\tfrac{1}{2}\right)_{n}}}P^{(\lambda-\frac{1}{2},% \lambda-\frac{1}{2})}_{n}\left(x\right)z^{n},}}
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    DLMF id
    DLMF:18.12.E4
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    constraint
    | z | < 1 𝑧 1 {\displaystyle{\displaystyle|z|<1}}
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