Difference between revisions of "Q-Cos"
From specialfunctionswiki
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The function $\mathrm{Cos}_q$ is defined by | The function $\mathrm{Cos}_q$ is defined by | ||
$$\mathrm{Cos}_q(z)=\dfrac{E_q(iz)+E_q(-iz)}{2},$$ | $$\mathrm{Cos}_q(z)=\dfrac{E_q(iz)+E_q(-iz)}{2},$$ | ||
| − | where $E_q$ denotes the [[q-exponential E|$q$-exponential $E$ | + | where $E_q$ denotes the [[q-exponential E|$q$-exponential $E$]]. |
=Properties= | =Properties= | ||
Revision as of 23:53, 3 May 2015
The function $\mathrm{Cos}_q$ is defined by $$\mathrm{Cos}_q(z)=\dfrac{E_q(iz)+E_q(-iz)}{2},$$ where $E_q$ denotes the $q$-exponential $E$.
Properties
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.
