DLMF:18.18.E30 (Q5820)

From DRMF
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:18.18.E30
No description defined

    Statements

    Defining formula
    ∑ ℓ = 0 n ℓ + 2 ⁢ λ 2 ⁢ λ ⁢ C ℓ ( λ ) ⁡ ( x ) ⁢ x n - ℓ = C n ( λ + 1 ) ⁡ ( x ) . superscript subscript ℓ 0 𝑛 ℓ 2 𝜆 2 𝜆 ultraspherical-Gegenbauer-polynomial 𝜆 ℓ 𝑥 superscript 𝑥 𝑛 ℓ ultraspherical-Gegenbauer-polynomial 𝜆 1 𝑛 𝑥 {\displaystyle{\displaystyle\sum_{\ell=0}^{n}\frac{\ell+2\lambda}{2\lambda}C^{% (\lambda)}_{\ell}\left(x\right)x^{n-\ell}=C^{(\lambda+1)}_{n}\left(x\right).}}
    0 references
    DLMF id
    DLMF:18.18.E30
    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.m2aedec
    0 references
    Q11744
    Defining formula
    ℓ ℓ {\displaystyle{\displaystyle\ell}}
    xml-id
    C18.S1.XMD4.m1qdec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1acdec
    0 references
    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1ydec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q5820&oldid=31615"