Formula:KLS:01.10:05

<< Formula:KLS:01.10:04

formula in Basic hypergeometric functions

Formula:KLS:01.10:06 >>

${\displaystyle{\displaystyle{\displaystyle\lim\limits_{q\rightarrow 1}\qHyperrphis{r}{s}@@{q^{a_{1}},\ldots,q^{a_{r}}}{q^{b_{1}},\ldots,q^{b_{s}}}{q}{(q-1)^{1+s-r}z}=\HyperpFq{r}{s}@@{a_{1},\ldots,a_{r}}{b_{1},\ldots,b_{s}}{z}}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle{{}_{r}\phi_{s}}}}}$ : basic hypergeometric (or ${\displaystyle{\displaystyle{\displaystyle q}}}$-hypergeometric) function : http://dlmf.nist.gov/17.4#E1
${\displaystyle{\displaystyle{\displaystyle{{}_{p}F_{q}}}}}$ : generalized hypergeometric function : http://dlmf.nist.gov/16.2#E1

Bibliography

Equation in Section 1.10 of KLS.

URL links

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<< Formula:KLS:01.10:04

formula in Basic hypergeometric functions

Formula:KLS:01.10:06 >>