Formula:KLS:01.08:27

<< Formula:KLS:01.08:26

formula in The q-shifted factorial

Formula:KLS:01.09:01 >>

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \frac{1-a^2q^{2n}}{1-a^2}=\frac{\qPochhammer{a^2q^2}{q^2}{n}}{\qPochhammer{a^2}{q^2}{n}} =\frac{\qPochhammer{aq}{q}{n}\qPochhammer{-aq}{q}{n}}{\qPochhammer{a}{q}{n}\qPochhammer{-a}{q}{n}} }}

Constraint(s)

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

Substitution(s)

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \qPochhammer{a^2}{q^2}{n}=\qPochhammer{a}{q}{n}\qPochhammer{-a}{q}{n}}} &

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \qPochhammer{a}{q}{n}=\frac{\qPochhammer{a}{q}{\infty}}{\qPochhammer{aq^n}{q}{\infty}} =\qPochhammer{a^{-1}q^{1-n}}{q}{n}(-a)^nq^{\binomial{n}{2}}}} &

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \qPochhammer{a}{q}{\infty}=\prod_{k=0}^{\infty}(1-aq^k) =\qPochhammer{a}{q^2}{\infty}\qPochhammer{aq}{q^2}{\infty}}}

Proof

We ask users to provide proof(s), reference(s) to proof(s), or further clarification on the proof(s) in this space.

Symbols List

& : logical and
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
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \binom{n}{k}}}  : binomial coefficient : http://dlmf.nist.gov/1.2#E1 http://dlmf.nist.gov/26.3#SS1.p1
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \Pi}}  : product : http://drmf.wmflabs.org/wiki/Definition:prod

Bibliography

Equation in Section 1.8 of KLS.

URL links

We ask users to provide relevant URL links in this space.

<< Formula:KLS:01.08:26

formula in The q-shifted factorial

Formula:KLS:01.09:01 >>