Formula:KLS:01.13:18

<< Formula:KLS:01.13:17

formula in Transformation formulas

Formula:KLS:01.13:19 >>

${\displaystyle{\displaystyle{\displaystyle\qHyperrphis{3}{2}@@{q^{-n},a,0}{b,c}{q}{q}=\frac{\left(b^{-1}q;q\right)_{\infty}}{\left(b^{-1}q^{1-n};q\right)_{\infty}}\,\qHyperrphis{2}{1}@@{q^{-n},a^{-1}c}{c}{q}{\frac{aq}{b}}}}}$

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
${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1

Bibliography

Equation in Section 1.13 of KLS.

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Formula:KLS:01.13:19 >>