Formula:KLS:01.11:10

<< Formula:KLS:01.11:09

formula in The q-binomial theorem and other summation formulas

The q-binomial theorem and other summation formulas >>

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \index{Jackson's summation formula}\index{Summation formula!Jackson}\index{Summation formula!for a very-well-poised $\qHyperrphis{6}{5}$} \qHyperrphis{6}{5}@@{q\sqrt{a},-q\sqrt{a},a,b,c,d}{\sqrt{a},-\sqrt{a},ab^{-1}q,ac^{-1}q,ad^{-1}q}{q}{\frac{aq}{bcd}} {}=\frac{\qPochhammer{aq,ab^{-1}c^{-1}q,ab^{-1}d^{-1}q,ac^{-1}d^{-1}q}{q}{\infty}} {\qPochhammer{ab^{-1}q,ac^{-1}q,ad^{-1}q,ab^{-1}c^{-1}d^{-1}q}{q}{\infty}} }}

Constraint(s)

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \left|\frac{aq}{bcd}\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:01.11:09

formula in The q-binomial theorem and other summation formulas

The q-binomial theorem and other summation formulas >>