DLMF:18.37.E7 (Q6055)

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DLMF:18.37.E7
No description defined

    Statements

    test
    P m , n α , β , γ ⁡ ( x , y ) = P m - n ( α , β + γ + 2 ⁢ n + 1 ) ⁡ ( 2 ⁢ x - 1 ) ⁢ x n ⁢ P n ( β , γ ) ⁡ ( 2 ⁢ x - 1 ⁢ y - 1 ) , triangle-orthogonal-polynomial-P 𝛼 𝛽 𝛾 𝑚 𝑛 𝑥 𝑦 Jacobi-polynomial-P 𝛼 𝛽 𝛾 2 𝑛 1 𝑚 𝑛 2 𝑥 1 superscript 𝑥 𝑛 Jacobi-polynomial-P 𝛽 𝛾 𝑛 2 superscript 𝑥 1 𝑦 1 {\displaystyle{\displaystyle P^{\alpha,\beta,\gamma}_{m,n}\left(x,y\right)=P^{% (\alpha,\beta+\gamma+2n+1)}_{m-n}\left(2x-1\right)\*x^{n}P^{(\beta,\gamma)}_{n% }\left(2x^{-1}y-1\right),}}
    0 references
    DLMF id
    DLMF:18.37.E7
    0 references
    constraint
    α , β , γ > - 1 𝛼 𝛽 𝛾 1 {\displaystyle{\displaystyle\alpha,\beta,\gamma>-1}}
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    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.m2aadec
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    Q11743
    test
    y 𝑦 {\displaystyle{\displaystyle y}}
    xml-id
    C18.S1.XMD1.m1bdec
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    Q11730
    test
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C18.S1.XMD5.m1fdec
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    Q11726
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1fdec
    0 references
    Q11727
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1bdec
    0 references
     
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