Formula:KLS:09.02:29

<< Formula:KLS:09.02:28

formula in Racah

Formula:KLS:09.02:30 >>

${\displaystyle{\displaystyle{\displaystyle\Bigg{[}(1-t)^{-\alpha-\beta-1}{}{{}_{4}F_{3}}\!\left({\frac{1}{2}(\alpha+\beta+1),\frac{1}{2}(\alpha+\beta+2),-x,x+\gamma+\delta+1\atop\alpha+1,\beta+\delta+1,\gamma+1};-\frac{4t}{(1-t)^{2}}\right)\Bigg{]}_{N}{}=\sum_{n=0}^{N}\frac{\pochhammer{\alpha+\beta+1}{n}}{n!}\Racah{n}@{\lambda(x)}{\alpha}{\beta}{\gamma}{\delta}t^{n}}}}$

Substitution(s)

${\displaystyle{\displaystyle{\displaystyle\lambda(x)=x(x+\gamma+\delta+1)}}}$

Proof

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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
${\displaystyle{\displaystyle{\displaystyle R_{n}}}}$ : Racah polynomial : http://dlmf.nist.gov/18.25#T1.t1.r4

Bibliography

Equation in Section 9.2 of KLS.

URL links

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<< Formula:KLS:09.02:28

formula in Racah

Formula:KLS:09.02:30 >>