DLMF:18.7.E14 (Q5582)

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DLMF:18.7.E14
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    Statements

    Defining formula
    P 2 ⁢ n + 1 ( α , α ) ⁡ ( x ) P 2 ⁢ n + 1 ( α , α ) ⁡ ( 1 ) = x ⁢ P n ( α , 1 2 ) ⁡ ( 2 ⁢ x 2 - 1 ) P n ( α , 1 2 ) ⁡ ( 1 ) . Jacobi-polynomial-P 𝛼 𝛼 2 𝑛 1 𝑥 Jacobi-polynomial-P 𝛼 𝛼 2 𝑛 1 1 𝑥 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+1}\left(x\right)}{P^% {(\alpha,\alpha)}_{2n+1}\left(1\right)}=\frac{xP^{(\alpha,\frac{1}{2})}_{n}% \left(2x^{2}-1\right)}{P^{(\alpha,\frac{1}{2})}_{n}\left(1\right)}.}}
    0 references
    DLMF id
    DLMF:18.7.E14
    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.m2ahdec
    0 references
     
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