Formula:KLS:09.08:06

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formula in Jacobi: Special cases

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${\displaystyle{\displaystyle{\displaystyle C^{\lambda}_{n}\left(x\right)=\frac{2^{n}{\left(\lambda\right)_{n}}}{n!}{\widehat{C}}^{\lambda}_{n}\left(x\right){x}}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle C^{\mu}_{n}}}}$ : ultraspherical/Gegenbauer polynomial : http://dlmf.nist.gov/18.3#T1.t1.r5
${\displaystyle{\displaystyle{\displaystyle(a)_{n}}}}$ : Pochhammer symbol : http://dlmf.nist.gov/5.2#iii
${\displaystyle{\displaystyle{\displaystyle{\widehat{C}}^{\mu}_{n}}}}$ : monic ultraspherical/Gegenbauer polynomial : http://drmf.wmflabs.org/wiki/Definition:monicUltra

Bibliography

Equation in Section 9.8 of KLS.

URL links

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formula in Jacobi: Special cases

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