Formula:KLS:01.11:06

<< Formula:KLS:01.11:05

formula in The q-binomial theorem and other summation formulas

Formula:KLS:01.11:07 >>

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \index{Summation formula!for a $\qHyperrphis{1}{1}$} \qHyperrphis{1}{1}@@{a}{c}{q}{\frac{c}{a}}=\frac{\qPochhammer{a^{-1}c}{q}{\infty}}{\qPochhammer{c}{q}{\infty}} }}

Constraint(s)

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle 0<|q|<1}}

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

Bibliography

Equation in Section 1.11 of KLS.

URL links

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<< Formula:KLS:01.11:05

formula in The q-binomial theorem and other summation formulas

Formula:KLS:01.11:07 >>