DLMF:18.18.E29 (Q5819)

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DLMF:18.18.E29
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    Statements

    Defining formula
    ∑ ℓ = 0 n C ℓ ( λ ) ⁡ ( x ) ⁢ C n - ℓ ( μ ) ⁡ ( x ) = C n ( λ + μ ) ⁡ ( x ) . superscript subscript ℓ 0 𝑛 ultraspherical-Gegenbauer-polynomial 𝜆 ℓ 𝑥 ultraspherical-Gegenbauer-polynomial 𝜇 𝑛 ℓ 𝑥 ultraspherical-Gegenbauer-polynomial 𝜆 𝜇 𝑛 𝑥 {\displaystyle{\displaystyle\sum_{\ell=0}^{n}C^{(\lambda)}_{\ell}\left(x\right% )C^{(\mu)}_{n-\ell}\left(x\right)=C^{(\lambda+\mu)}_{n}\left(x\right).}}
    0 references
    DLMF id
    DLMF:18.18.E29
    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.m2addec
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    Q11744
    Defining formula
    ℓ ℓ {\displaystyle{\displaystyle\ell}}
    xml-id
    C18.S1.XMD4.m1pdec
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    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1abdec
    0 references
     
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