Difference between revisions of "Q-Euler formula for E sub q"
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The following formula holds: | The following formula holds: | ||
$$E_q(iz)=\mathrm{Cos}_q(z)+i\mathrm{Sin}_q(z),$$ | $$E_q(iz)=\mathrm{Cos}_q(z)+i\mathrm{Sin}_q(z),$$ | ||
| − | where $E_q$ is the [[q-exponential E|$q$-exponential $ | + | where $E_q$ is the [[q-exponential E sub q|$q$-exponential $E_q$]], $\mathrm{Cos}_q$ is the [[q-Cos|$q$-$\mathrm{Cos}$]] function and $\mathrm{Sin}_q$ is the [[q-Sin|$q$-$\mathrm{Sin}$]] function. |
==Proof== | ==Proof== | ||
Latest revision as of 23:10, 26 June 2016
Theorem
The following formula holds: $$E_q(iz)=\mathrm{Cos}_q(z)+i\mathrm{Sin}_q(z),$$ where $E_q$ is the $q$-exponential $E_q$, $\mathrm{Cos}_q$ is the $q$-$\mathrm{Cos}$ function and $\mathrm{Sin}_q$ is the $q$-$\mathrm{Sin}$ function.
