DLMF:18.35.E2 (Q6041)

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DLMF:18.35.E2
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    Statements

    Defining formula
    ( n + 1 ) ⁢ P n + 1 ( λ ) ⁡ ( x ; a , b ) = 2 ⁢ ( ( n + λ + a ) ⁢ x + b ) ⁢ P n ( λ ) ⁡ ( x ; a , b ) - ( n + 2 ⁢ λ - 1 ) ⁢ P n - 1 ( λ ) ⁡ ( x ; a , b ) , 𝑛 1 Pollaczek-polynomial-P 𝜆 𝑛 1 𝑥 𝑎 𝑏 2 𝑛 𝜆 𝑎 𝑥 𝑏 Pollaczek-polynomial-P 𝜆 𝑛 𝑥 𝑎 𝑏 𝑛 2 𝜆 1 Pollaczek-polynomial-P 𝜆 𝑛 1 𝑥 𝑎 𝑏 {\displaystyle{\displaystyle(n+1)P^{(\lambda)}_{n+1}\left(x;a,b\right)={2((n+% \lambda+a)x+b)}P^{(\lambda)}_{n}\left(x;a,b\right)-{(n+2\lambda-1)}P^{(\lambda% )}_{n-1}\left(x;a,b\right),}}
    0 references
    DLMF id
    DLMF:18.35.E2
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    constraint
    n = 0 , 1 , … 𝑛 0 1 … {\displaystyle{\displaystyle n=0,1,\dots}}
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    Symbols used
    Pollaczek polynomial
    Defining formula
    P n ( λ ) ⁡ ( x ; a , b ) Pollaczek-polynomial-P 𝜆 𝑛 𝑥 𝑎 𝑏 {\displaystyle{\displaystyle P^{(\NVar{\lambda})}_{\NVar{n}}\left(\NVar{x};% \NVar{a},\NVar{b}\right)}}
    xml-id
    C18.S35.E4.m2aadec
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    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1dec
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    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1adec
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