Difference between revisions of "Q-exponential e sub q"
From specialfunctionswiki
| Line 1: | Line 1: | ||
The $q$-exponential $e_q$ is defined by the formula | The $q$-exponential $e_q$ is defined by the formula | ||
| − | $$e_q(z) = | + | $$e_q(z) = $$ |
=Properties= | =Properties= | ||
{{:Q-Euler formula for e sub q}} | {{:Q-Euler formula for e sub q}} | ||
Revision as of 17:50, 20 May 2015
The $q$-exponential $e_q$ is defined by the formula $$e_q(z) = $$
Contents
Properties
Theorem
The following formula holds: $$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.
