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DLMF:18.7.E13 - MaRDI portal

DLMF:18.7.E13 (Q6278)

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DLMF:18.7.E13
No description defined

    Statements

    DLMF defining formula
    P 2 ⁢ n ( α , α ) ⁡ ( x ) P 2 ⁢ n ( α , α ) ⁡ ( 1 ) = P n ( α , - 1 2 ) ⁡ ( 2 ⁢ x 2 - 1 ) P n ( α , - 1 2 ) ⁡ ( 1 ) , Jacobi-polynomial-P 𝛼 𝛼 2 𝑛 𝑥 Jacobi-polynomial-P 𝛼 𝛼 2 𝑛 1 Jacobi-polynomial-P 𝛼 1 2 𝑛 2 superscript 𝑥 2 1 Jacobi-polynomial-P 𝛼 1 2 𝑛 1 {\displaystyle{\displaystyle\frac{P^{(\alpha,\alpha)}_{2n}\left(x\right)}{P^{(% \alpha,\alpha)}_{2n}\left(1\right)}=\frac{P^{(\alpha,-\frac{1}{2})}_{n}\left(2% x^{2}-1\right)}{P^{(\alpha,-\frac{1}{2})}_{n}\left(1\right)},}}
    0 references
    Symbols used
    Jacobi polynomial
    DLMF 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.m2agdec
    0 references
    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1ldec
    0 references
    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1ldec
    0 references
     
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