Formula:KLS:09.08:67

<< Formula:KLS:09.08:66

formula in Jacobi: Special cases

Formula:KLS:09.08:68 >>

${\displaystyle{\displaystyle{\displaystyle(1-xt)^{-\gamma}\,\HyperpFq{2}{1}@@{\frac{1}{2}\gamma,\frac{1}{2}\gamma+\frac{1}{2}}{\frac{1}{2}}{\frac{(x^{2}-1)t^{2}}{(1-xt)^{2}}}=\sum_{n=0}^{\infty}\frac{{\left(\gamma\right)_{n}}}{n!}T_{n}\left(x\right)t^{n}}}}$

Constraint(s)

${\displaystyle{\displaystyle{\displaystyle\gamma}}}$ arbitrary

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
${\displaystyle{\displaystyle{\displaystyle(a)_{n}}}}$ : Pochhammer symbol : http://dlmf.nist.gov/5.2#iii
${\displaystyle{\displaystyle{\displaystyle T_{n}}}}$ : Chebyshev polynomial of the first kind : http://dlmf.nist.gov/18.3#T1.t1.r8

Bibliography

Equation in Section 9.8 of KLS.

URL links

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

<< Formula:KLS:09.08:66

formula in Jacobi: Special cases

Formula:KLS:09.08:68 >>