DLMF:18.9.E7 (Q5603)

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DLMF:18.9.E7
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    Statements

    Defining formula
    ( n + λ ) ⁢ C n ( λ ) ⁡ ( x ) = λ ⁢ ( C n ( λ + 1 ) ⁡ ( x ) - C n - 2 ( λ + 1 ) ⁡ ( x ) ) , 𝑛 𝜆 ultraspherical-Gegenbauer-polynomial 𝜆 𝑛 𝑥 𝜆 ultraspherical-Gegenbauer-polynomial 𝜆 1 𝑛 𝑥 ultraspherical-Gegenbauer-polynomial 𝜆 1 𝑛 2 𝑥 {\displaystyle{\displaystyle(n+\lambda)C^{(\lambda)}_{n}\left(x\right)=\lambda% \left(C^{(\lambda+1)}_{n}\left(x\right)-C^{(\lambda+1)}_{n-2}\left(x\right)% \right),}}
    0 references
    DLMF id
    DLMF:18.9.E7
    0 references
    Symbols used
    Q11475
    Defining formula
    C n ( λ ) ⁡ ( x ) ultraspherical-Gegenbauer-polynomial 𝜆 𝑛 𝑥 {\displaystyle{\displaystyle C^{(\NVar{\lambda})}_{\NVar{n}}\left(\NVar{x}% \right)}}
    xml-id
    C18.S3.T1.t1.r3.m2aadec
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