Q-Cos
From specialfunctionswiki
The function $\mathrm{Cos}_q$ is defined by $$\mathrm{Cos}_q(z)=\dfrac{E_q(iz)+E_q(-iz)}{2},$$ where $E_q$ denotes the $q$-exponential $E$.
Properties
q-Euler formula for E sub q
q-derivative of q-Cos