Formula:KLS:01.11:04

<< Formula:KLS:01.11:03

formula in The q-binomial theorem and other summation formulas

Formula:KLS:01.11:05 >>

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \index{q-Vandermonde summation formula@$q$-Vandermonde summation formula}\index{Summation formula!q-Vandermonde@$q$-Vandermonde}\index{q-Chu-Vandermonde summation formula@$q$-Chu-Vandermonde summation formula}\index{Summation formula!q-Chu-Vandermonde@$q$-Chu-Vandermonde} \qHyperrphis{2}{1}@@{q^{-n},b}{c}{q}{\frac{cq^n}{b}}=\frac{\qPochhammer{b^{-1}c}{q}{n}}{\qPochhammer{c}{q}{n}} }}

Constraint(s)

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle n=0,1,2,\ldots}}

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:01.11:03

formula in The q-binomial theorem and other summation formulas

Formula:KLS:01.11:05 >>