DLMF:18.18.E16 (Q5806)

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DLMF:18.18.E16
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    C n ( μ ) ( x ) = = 0 n / 2 λ + n - 2 λ ( μ ) n - ( λ + 1 ) n - ( μ - λ ) ! C n - 2 ( λ ) ( x ) , ultraspherical-Gegenbauer-polynomial 𝜇 𝑛 𝑥 superscript subscript 0 𝑛 2 𝜆 𝑛 2 𝜆 Pochhammer 𝜇 𝑛 Pochhammer 𝜆 1 𝑛 Pochhammer 𝜇 𝜆 ultraspherical-Gegenbauer-polynomial 𝜆 𝑛 2 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),}}
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