Formula:KLS:01.09:01

<< The q-shifted factorial

formula in The q-gamma function and q-binomial coefficients

Formula:KLS:01.09:02 >>

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \index{q-Gamma function@$q$-Gamma function} \qGamma{q}@{x}:=\frac{\qPochhammer{q}{q}{\infty}}{\qPochhammer{q^x}{q}{\infty}}(1-q)^{1-x} }}

Constraint(s)

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle 0<q<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 \Gamma_{q}}}  : Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle q}} -gamma function : http://dlmf.nist.gov/5.18#E4
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 1.9 of KLS.

URL links

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<< The q-shifted factorial

formula in The q-gamma function and q-binomial coefficients

Formula:KLS:01.09:02 >>