The q-analog of the factorial (by analogy with the q-gamma function). For k an integer, the q-factorial is defined by [k]_q ! | = | faq(k, q) | = | 1(1 + q)(1 + q + q^2)...(1 + q + ... + q^(k - 1)) | = | (q;q)_k/(1 - q)^k (Koepf 1998, p. 26). For k element N, [k]_q ! = Γ_q(k + 1), where Γ_q(k + 1) is the q-gamma function. q-factorials are implemented in the Wolfram Language as QFactorial[n, q].

q-beta function | q-binomial coefficient | q-bracket | q-cosine | q-gamma function | q-pi | q-sine