Formula:KLS:01.13:26

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formula in Transformation formulas

Formula:KLS:01.13:27 >>

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \index{Sears' transformation formula}\index{Transformation formula!Sears} \qHyperrphis{4}{3}@@{q^{-n},a,b,c}{d,e,f}{q}{q} {}=\frac{\qPochhammer{a^{-1}e,a^{-1}f}{q}{n}}{\qPochhammer{e,f}{q}{n}}a^n\,\qHyperrphis{4}{3}@@{q^{-n},a,b^{-1}d,c^{-1}d}{d,a\expe^{-1}q^{1-n},af^{-1}q^{1-n}}{q}{q} {} }}

Proof

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Symbols List

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle {{}_{r}\phi_{s}}}}  : basic hypergeometric (or Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle q}} -hypergeometric) function : http://dlmf.nist.gov/17.4#E1
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle (a;q)_n}}  : Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle q}} -Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\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.

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