Difference between revisions of "Q-Euler formula for E sub q"
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| − | + | ==Theorem== | |
| − | + | 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 $E$]], $\mathrm{Cos}_q$ is the [[q-Cos|$q$-$\mathrm{Cos}$]] function and $\mathrm{Sin}_q$ is the [[q-Sin|$q$-$\mathrm{Sin}$]] function. | where $E_q$ is the [[q-exponential E|$q$-exponential $E$]], $\mathrm{Cos}_q$ is the [[q-Cos|$q$-$\mathrm{Cos}$]] function and $\mathrm{Sin}_q$ is the [[q-Sin|$q$-$\mathrm{Sin}$]] function. | ||
| − | + | ||
| − | + | ==Proof== | |
| − | + | ||
| − | + | ==References== | |
| + | |||
| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
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 $E$, $\mathrm{Cos}_q$ is the $q$-$\mathrm{Cos}$ function and $\mathrm{Sin}_q$ is the $q$-$\mathrm{Sin}$ function.
