Formula:KLS:01.13:15

<< Formula:KLS:01.13:14

formula in Transformation formulas

Formula:KLS:01.13:16 >>

${\displaystyle{\displaystyle{\displaystyle\qHyperrphis{2}{1}@@{q^{-n},b}{c}{q}{z}=\frac{\left(b;q\right)_{n}}{\left(c;q\right)_{n}}q^{-n-\binomial{n}{2}}(-z)^{n}\ \qHyperrphis{2}{1}@@{q^{-n},c^{-1}q^{1-n}}{b^{-1}q^{1-n}}{q}{\frac{cq^{n+1}}{bz}}}}}$

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
${\displaystyle{\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{n}{k}}}}$ : binomial coefficient : http://dlmf.nist.gov/1.2#E1 http://dlmf.nist.gov/26.3#SS1.p1

Bibliography

Equation in Section 1.13 of KLS.

URL links

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