A q-analog of the gamma function defined by Γ_q(x) congruent (q;q)_∞/(q^x ;q)_∞ (1 - q)^(1 - x), where (x, q)_∞ is a q-Pochhammer symbol. The q-gamma function satisfies lim_(q->1^-) Γ_q(x) = Γ(x), where Γ(z) is the gamma function. The q-gamma function is implemented in the Wolfram Language as QGamma[z, q].

gamma function | q-beta function | q-factorial | q-Pochhammer symbol