The q-analog of pi π_q can be defined by setting a = 0 in the q-factorial [a]_q ! = 1(1 + q)(1 + q + q^2)...(1 + q + ... + q^(a - 1)) to obtain 1 = sin_q^*(1/2 π) = π_q/(([-1/2]_q^2 !)^2 q^(1/4)), where sin_q^* z is Gosper's q-sine, so

pi | q-analog | q-cosine | q-exponential function | q-factorial | q-sine | Wallis formula