DLMF:18.7.E6 (Q5574)

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DLMF:18.7.E6
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    Statements

    Defining formula
    W n ⁡ ( x ) = P n ( - 1 2 , 1 2 ) ⁡ ( x ) / P n ( - 1 2 , 1 2 ) ⁡ ( 1 ) . Chebyshev-polynomial-fourth-kind-W 𝑛 𝑥 Jacobi-polynomial-P 1 2 1 2 𝑛 𝑥 Jacobi-polynomial-P 1 2 1 2 𝑛 1 {\displaystyle{\displaystyle W_{n}\left(x\right)=\ifrac{P^{(-\frac{1}{2},\frac% {1}{2})}_{n}\left(x\right)}{P^{(-\frac{1}{2},\frac{1}{2})}_{n}\left(1\right)}.}}
    0 references
    DLMF id
    DLMF:18.7.E6
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    Symbols used
    Q11746
    Defining formula
    W n ⁡ ( x ) Chebyshev-polynomial-fourth-kind-W 𝑛 𝑥 {\displaystyle{\displaystyle W_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C18.S3.T1.t1.r7.m2adec
    0 references
    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
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1edec
    0 references
     
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