Formula:KLS:01.11:09

<< Formula:KLS:01.11:08

formula in The q-binomial theorem and other summation formulas

Formula:KLS:01.11:10 >>

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

Constraint(s)

${\displaystyle{\displaystyle{\displaystyle n=0,1,2,\ldots}}}$

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 1.11 of KLS.

URL links

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<< Formula:KLS:01.11:08

formula in The q-binomial theorem and other summation formulas

Formula:KLS:01.11:10 >>