Formula:KLS:01.11:06: Difference between revisions

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Latest revision as of 08:33, 22 December 2019


\qHyperrphis 11 @ @ a c q c a = ( a - 1 c ; q ) ( c ; q ) \qHyperrphis 11 @ @ 𝑎 𝑐 𝑞 𝑐 𝑎 q-Pochhammer-symbol superscript 𝑎 1 𝑐 𝑞 q-Pochhammer-symbol 𝑐 𝑞 {\displaystyle{\displaystyle{\displaystyle{}\qHyperrphis{1}{1}@@{a}{c}{q}{% \frac{c}{a}}=\frac{\left(a^{-1}c;q\right)_{\infty}}{\left(c;q\right)_{\infty}}% }}}

Constraint(s)

0 < | q | < 1 0 𝑞 1 {\displaystyle{\displaystyle{\displaystyle 0<|q|<1}}}


Proof

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Symbols List

ϕ s r subscript subscript italic-ϕ 𝑠 𝑟 {\displaystyle{\displaystyle{\displaystyle{{}_{r}\phi_{s}}}}}  : basic hypergeometric (or q 𝑞 {\displaystyle{\displaystyle{\displaystyle q}}} -hypergeometric) function : http://dlmf.nist.gov/17.4#E1
( a ; q ) n subscript 𝑎 𝑞 𝑛 {\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}  : q 𝑞 {\displaystyle{\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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