Formula:KLS:09.08:19

<< Formula:KLS:09.08:18

formula in Jacobi: Special cases

Formula:KLS:09.08:20 >>

${\displaystyle{\displaystyle{\displaystyle C^{\lambda}_{2n}\left(x\right)=\frac{{\left(\lambda\right)_{n}}}{{\left(\frac{1}{2}\right)_{n}}}P^{(\lambda-\frac{1}{2},-\frac{1}{2})}_{n}\left(2x^{2}-1\right)}}}$

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
${\displaystyle{\displaystyle{\displaystyle P^{(\alpha,\beta)}_{n}}}}$ : Jacobi polynomial : http://dlmf.nist.gov/18.3#T1.t1.r3

Bibliography

Equation in Section 9.8 of KLS.

URL links

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<< Formula:KLS:09.08:18

formula in Jacobi: Special cases

Formula:KLS:09.08:20 >>