Formula:KLS:01.13:17

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formula in Transformation formulas

Formula:KLS:01.13:18 >>

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

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:01.13:18 >>