A q-analog of the beta function B(a, b) | = | integral_0^1 t^(a - 1) (1 - t)^(b - 1) d t | = | (Γ(a) Γ(b))/(Γ(a + b)), where Γ(z) is a gamma function, is given by B_q(a, b) | congruent | integral_0^1 t^(b - 1) (q t;q)_(a - 1) d(q, t) | = | (Γ_q(a) Γ_q(b))/(Γ_q(a + b)), where Γ_q(a) is a q-gamma function, (a;q)_n is a q-Pochhammer symbol coefficient, and integral_0^1 f(x) d(q, x) = (1 - q) sum_(i = 0)^∞ f(q^i) q^i

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