Formula:KLS:01.13:26

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formula in Transformation formulas

Formula:KLS:01.13:27 >>

${\displaystyle{\displaystyle{\displaystyle{}{}\qHyperrphis{4}{3}@@{q^{-n},a,b,c}{d,e,f}{q}{q}{}=\frac{\left(a^{-1}e,a^{-1}f;q\right)_{n}}{\left(e,f;q\right)_{n}}a^{n}\,\qHyperrphis{4}{3}@@{q^{-n},a,b^{-1}d,c^{-1}d}{d,a{\mathrm{e}^{-1}}q^{1-n},af^{-1}q^{1-n}}{q}{q}{}}}}$

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
${\displaystyle{\displaystyle{\displaystyle\mathrm{e}}}}$ : the base of the natural logarithm : http://dlmf.nist.gov/4.2.E11

Bibliography

Equation in Section 1.13 of KLS.

URL links

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