Q-cos sub q

The function $\cos_q$ is defined for $|z|<1$ by $$\cos_q(z)=\dfrac{e_q(iz)+e_q(-iz)}{2},$$ where $e_q$ denotes the $q$-exponential $e$ and $(q;q)_{2k}$ denotes the $q$-Pochhammer symbol.

Properties

q-Euler formula for e sub q

External links

[1]

References

• 2012: Thomas Ernst: A Comprehensive Treatment of q-Calculus ... (previous): $(6.202)$