Formula:KLS:01.13:22

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formula in Transformation formulas

Formula:KLS:01.13:23 >>

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

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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