Difference between revisions of "Q-Euler formula for e sub q"
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| − | + | ==Theorem== | |
| − | + | 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 $e$]], $\cos_q$ is the [[q-cos|$q$-$\cos$]] function and $\sin_q$ is the [[q-sin|$q$-$\sin$]] function. | where $e_q$ is the [[q-exponential e|$q$-exponential $e$]], $\cos_q$ is the [[q-cos|$q$-$\cos$]] function and $\sin_q$ is the [[q-sin|$q$-$\sin$]] function. | ||
| − | + | ||
| − | + | ==Proof== | |
| − | + | ||
| − | + | ==References== | |
| + | |||
| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Revision as of 21:20, 4 July 2016
Theorem
The following formula holds: $$e_q(iz)=\cos_q(z)+i\sin_q(z),$$ where $e_q$ is the $q$-exponential $e$, $\cos_q$ is the $q$-$\cos$ function and $\sin_q$ is the $q$-$\sin$ function.
