Formula:KLS:09.08:14

<< Formula:KLS:09.08:13

formula in Jacobi: Special cases

Formula:KLS:09.08:15 >>

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

Proof

We ask users to provide proof(s), reference(s) to proof(s), or further clarification on the proof(s) in this space.

Symbols List

${\displaystyle{\displaystyle{\displaystyle{{}_{p}F_{q}}}}}$ : generalized hypergeometric function : http://dlmf.nist.gov/16.2#E1
${\displaystyle{\displaystyle{\displaystyle\Sigma}}}$ : 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
${\displaystyle{\displaystyle{\displaystyle(a)_{n}}}}$ : Pochhammer symbol : http://dlmf.nist.gov/5.2#iii

Bibliography

Equation in Section 9.8 of KLS.

URL links

We ask users to provide relevant URL links in this space.

<< Formula:KLS:09.08:13

formula in Jacobi: Special cases

Formula:KLS:09.08:15 >>