# Formula:KLS:14.12:18

$\displaystyle {\displaystyle \qHyperrphis{0}{1}@@{-}{aq}{q}{aqxt}\,\qHyperrphis{2}{1}@@{x^{-1},0}{bq}{q}{xt}=\sum_{n=0}^{\infty} \frac{(-1)^nq^{\binomial{n}{2}}}{\qPochhammer{bq,q}{q}{n}}\littleqJacobi{n}@{x}{a}{b}{q}t^n }$

## Proof

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## Symbols List

$\displaystyle {\displaystyle {{}_{r}\phi_{s}}}$  : basic hypergeometric (or $\displaystyle {\displaystyle q}$ -hypergeometric) function : http://dlmf.nist.gov/17.4#E1
$\displaystyle {\displaystyle \Sigma}$  : sum : http://drmf.wmflabs.org/wiki/Definition:sum
$\displaystyle {\displaystyle \binom{n}{k}}$  : binomial coefficient : http://dlmf.nist.gov/1.2#E1 http://dlmf.nist.gov/26.3#SS1.p1
$\displaystyle {\displaystyle (a;q)_n}$  : $\displaystyle {\displaystyle q}$ -Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1
$\displaystyle {\displaystyle p_{n}}$  : little $\displaystyle {\displaystyle q}$ -Jacobi polynomial : http://drmf.wmflabs.org/wiki/Definition:littleqJacobi