There are several q-analogs of the sine function. The two natural definitions of the q-sine defined by Koekoek and Swarttouw are given by sin_q(z) | = | sum_(n = 0)^∞ ((-1)^n z^(2n + 1))/(q;q)_(2n + 1) | = | (e_q(i z) - e_q(-i z))/(2i) Sin_q(z) | = | (E_q(i z) - E_q(-i z))/(2i), where e_q(z) and E_q(z) are q-exponential functions.

q-cosine | q-exponential function | q-factorial | q-pi