Formula:KLS:09.08:12

<< Formula:KLS:09.08:11

formula in Jacobi: Special cases

Formula:KLS:09.08:13 >>

${\displaystyle{\displaystyle{\displaystyle(1-2xt+t^{2})^{-\lambda}=\sum_{n=0}^{\infty}C^{\lambda}_{n}\left(x\right)t^{n}}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle\Sigma}}}$ : sum : http://drmf.wmflabs.org/wiki/Definition:sum
${\displaystyle{\displaystyle{\displaystyle C^{\mu}_{n}}}}$ : ultraspherical/Gegenbauer polynomial : http://dlmf.nist.gov/18.3#T1.t1.r5

Bibliography

Equation in Section 9.8 of KLS.

URL links

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<< Formula:KLS:09.08:11

formula in Jacobi: Special cases

Formula:KLS:09.08:13 >>