DLMF:18.18.E16 (Q5806)

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DLMF:18.18.E16
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    Statements

    Defining formula
    C n ( μ ) ⁡ ( x ) = ∑ ℓ = 0 ⌊ n / 2 ⌋ λ + n - 2 ⁢ ℓ λ ⁢ ( μ ) n - ℓ ( λ + 1 ) n - ℓ ⁢ ( μ - λ ) ℓ ℓ ! ⁢ C n - 2 ⁢ ℓ ( λ ) ⁡ ( x ) , ultraspherical-Gegenbauer-polynomial 𝜇 𝑛 𝑥 superscript subscript ℓ 0 𝑛 2 𝜆 𝑛 2 ℓ 𝜆 Pochhammer 𝜇 𝑛 ℓ Pochhammer 𝜆 1 𝑛 ℓ Pochhammer 𝜇 𝜆 ℓ ℓ ultraspherical-Gegenbauer-polynomial 𝜆 𝑛 2 ℓ 𝑥 {\displaystyle{\displaystyle C^{(\mu)}_{n}\left(x\right)=\sum_{\ell=0}^{\left% \lfloor n/2\right\rfloor}\frac{\lambda+n-2\ell}{\lambda}\frac{{\left(\mu\right% )_{n-\ell}}}{{\left(\lambda+1\right)_{n-\ell}}}\frac{{\left(\mu-\lambda\right)% _{\ell}}}{\ell!}C^{(\lambda)}_{n-2\ell}\left(x\right),}}
    0 references
    DLMF id
    DLMF:18.18.E16
    0 references
    Symbols used
    Q10759
    Defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1addec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5ahdec
    0 references
    Q11169
    Defining formula
    ⌊ x ⌋ 𝑥 {\displaystyle{\displaystyle\left\lfloor\NVar{x}\right\rfloor}}
    xml-id
    introduction.Sx4.p1.t1.r17.m4aadec
    0 references
    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
    0 references
    Q11744
    Defining formula
    ℓ ℓ {\displaystyle{\displaystyle\ell}}
    xml-id
    C18.S1.XMD4.m1fdec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1odec
    0 references
    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1ldec
    0 references
     
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