Formula:KLS:01.11:03

<< Formula:KLS:01.11:02

formula in The q-binomial theorem and other summation formulas

Formula:KLS:01.11:04 >>

${\displaystyle{\displaystyle{\displaystyle{}{}\qHyperrphis{2}{1}@@{a,b}{c}{q}{\frac{c}{ab}}=\frac{\left(a^{-1}c,b^{-1}c;q\right)_{\infty}}{\left(c,a^{-1}b^{-1}c;q\right)_{\infty}},\quad 0<|q|<1}}}$

Constraint(s)

${\displaystyle{\displaystyle{\displaystyle\left|\frac{c}{ab}\right|<1}}}$

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:01.11:02

formula in The q-binomial theorem and other summation formulas

Formula:KLS:01.11:04 >>