DLMF:18.18.E25 (Q5815)

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DLMF:18.18.E25
No description defined

    Statements

    Defining formula
    P n ( α , β ) ⁡ ( x ) P n ( α , β ) ⁡ ( 1 ) ⁢ P n ( α , β ) ⁡ ( y ) P n ( α , β ) ⁡ ( 1 ) = ∑ ℓ = 0 n b n , ℓ ⁢ ( x + y ) ℓ ⁢ P ℓ ( α , β ) ⁡ ( ( 1 + x ⁢ y ) / ( x + y ) ) P ℓ ( α , β ) ⁡ ( 1 ) , Jacobi-polynomial-P 𝛼 𝛽 𝑛 𝑥 Jacobi-polynomial-P 𝛼 𝛽 𝑛 1 Jacobi-polynomial-P 𝛼 𝛽 𝑛 𝑦 Jacobi-polynomial-P 𝛼 𝛽 𝑛 1 superscript subscript ℓ 0 𝑛 subscript 𝑏 𝑛 ℓ superscript 𝑥 𝑦 ℓ Jacobi-polynomial-P 𝛼 𝛽 ℓ 1 𝑥 𝑦 𝑥 𝑦 Jacobi-polynomial-P 𝛼 𝛽 ℓ 1 {\displaystyle{\displaystyle\frac{P^{(\alpha,\beta)}_{n}\left(x\right)}{P^{(% \alpha,\beta)}_{n}\left(1\right)}\frac{P^{(\alpha,\beta)}_{n}\left(y\right)}{P% ^{(\alpha,\beta)}_{n}\left(1\right)}=\sum_{\ell=0}^{n}b_{n,\ell}(x+y)^{\ell}\*% \frac{P^{(\alpha,\beta)}_{\ell}\left(\ifrac{(1+xy)}{(x+y)}\right)}{P^{(\alpha,% \beta)}_{\ell}\left(1\right)},}}
    0 references
    DLMF id
    DLMF:18.18.E25
    0 references
    Symbols used
    Q11660
    Defining formula
    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.m2aedec
    0 references
    Q11743
    Defining formula
    y 𝑦 {\displaystyle{\displaystyle y}}
    xml-id
    C18.S1.XMD1.m1dec
    0 references
    Q11744
    Defining formula
    ℓ ℓ {\displaystyle{\displaystyle\ell}}
    xml-id
    C18.S1.XMD4.m1ndec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1xdec
    0 references
    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1tdec
    0 references
     
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