Q-Euler formula for E sub q

From specialfunctionswiki
Revision as of 23:10, 26 June 2016 by Tom (talk | contribs)
Jump to: navigation, search

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.

Proof

References