Formula:KLS:01.13:14

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Formula:KLS:01.13:15 >>

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

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
${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-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.

URL links

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