Formula:KLS:01.11:03

<< Formula:KLS:01.11:02

formula in The q-binomial theorem and other summation formulas

Formula:KLS:01.11:04 >>

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \index{q-Gauss summation formula@$q$-Gauss summation formula}\index{Summation formula!q-Gauss@$q$-Gauss} \qHyperrphis{2}{1}@@{a,b}{c}{q}{\frac{c}{ab}}=\frac{\qPochhammer{a^{-1}c,b^{-1}c}{q}{\infty}} {\qPochhammer{c,a^{-1}b^{-1}c}{q}{\infty}},\quad 0<|q|<1 }}

Constraint(s)

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \left|\frac{c}{ab}\right|<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:01.11:02

formula in The q-binomial theorem and other summation formulas

Formula:KLS:01.11:04 >>