DLMF:18.12.E1 (Q5643)

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DLMF:18.12.E1
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    Statements

    test
    2 α + β R ⁢ ( 1 + R - z ) α ⁢ ( 1 + R + z ) β = ∑ n = 0 ∞ P n ( α , β ) ⁡ ( x ) ⁢ z n , superscript 2 𝛼 𝛽 𝑅 superscript 1 𝑅 𝑧 𝛼 superscript 1 𝑅 𝑧 𝛽 superscript subscript 𝑛 0 Jacobi-polynomial-P 𝛼 𝛽 𝑛 𝑥 superscript 𝑧 𝑛 {\displaystyle{\displaystyle\frac{2^{\alpha+\beta}}{R(1+R-z)^{\alpha}(1+R+z)^{% \beta}}=\sum_{n=0}^{\infty}P^{(\alpha,\beta)}_{n}\left(x\right)z^{n},}}
    0 references
    DLMF id
    DLMF:18.12.E1
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    constraint
    | z | < 1 𝑧 1 {\displaystyle{\displaystyle|z|<1}}
    0 references
    Symbols used
    Q11660
    test
    P n ( α , β ) ⁡ ( x ) Jacobi-polynomial-P 𝛼 𝛽 𝑛 𝑥 {\displaystyle{\displaystyle P^{(\NVar{\alpha},\NVar{\beta})}_{\NVar{n}}\left(% \NVar{x}\right)}}
    xml-id
    C18.S3.T1.t1.r2.m2adec
    0 references
     
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