Formula:KLS:01.11:10

<< Formula:KLS:01.11:09

formula in The q-binomial theorem and other summation formulas

The q-binomial theorem and other summation formulas >>

${\displaystyle{\displaystyle{\displaystyle{}{}{}\qHyperrphis{6}{5}@@{q\sqrt{a},-q\sqrt{a},a,b,c,d}{\sqrt{a},-\sqrt{a},ab^{-1}q,ac^{-1}q,ad^{-1}q}{q}{\frac{aq}{bcd}}{}=\frac{\left(aq,ab^{-1}c^{-1}q,ab^{-1}d^{-1}q,ac^{-1}d^{-1}q;q\right)_{\infty}}{\left(ab^{-1}q,ac^{-1}q,ad^{-1}q,ab^{-1}c^{-1}d^{-1}q;q\right)_{\infty}}}}}$

Constraint(s)

${\displaystyle{\displaystyle{\displaystyle\left|\frac{aq}{bcd}\right|<1}}}$

Proof

We ask users to provide proof(s), reference(s) to proof(s), or further clarification on the proof(s) in this space.

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

We ask users to provide relevant URL links in this space.

<< Formula:KLS:01.11:09

formula in The q-binomial theorem and other summation formulas

The q-binomial theorem and other summation formulas >>