Difference between revisions of "Q-Euler formula for e sub q"
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The following formula holds: | The following formula holds: | ||
$$e_q(iz)=\cos_q(z)+i\sin_q(z),$$ | $$e_q(iz)=\cos_q(z)+i\sin_q(z),$$ | ||
| − | where $e_q$ is the [[q-exponential e|$q$-exponential $ | + | where $e_q$ is the [[q-exponential e sub q|$q$-exponential $e_q$]], $\cos_q$ is the [[q-cos sub q|$q$-$\cos$]] function and $\sin_q$ is the [[q-sin sub q|$q$-$\sin$]] function. |
==Proof== | ==Proof== | ||
Latest revision as of 15:36, 11 July 2016
Theorem
The following formula holds: $$e_q(iz)=\cos_q(z)+i\sin_q(z),$$ where $e_q$ is the $q$-exponential $e_q$, $\cos_q$ is the $q$-$\cos$ function and $\sin_q$ is the $q$-$\sin$ function.
