Latest revision as of 23:28, 26 June 2016

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

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+__NOTOC__
 The function $\mathrm{Cos}_q$ is defined by
 $$\mathrm{Cos}_q(z)=\dfrac{E_q(iz)+E_q(-iz)}{2},$$
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 =Properties=
-{{:q-Euler formula for E sub q}}
+[[q-Euler formula for E sub q]]<br />
-<div class="toccolours mw-collapsible mw-collapsed">
+[[q-derivative of q-Cosine]]<br />
-<strong>Theorem:</strong> The following formula holds:
-$$D_q \mathrm{Cos}_q(az) = -a \mathrm{Sin}_q(az),$$
+=External links=
-where $D_q$ denotes the [[q-difference operator]], $\mathrm{Cos}$ denotes the [[Q-Cos|$q$-Cosine function]], and $\mathrm{Sin}$ denotes the [[Q-Sin|$q$-Sine function]].
+[http://homepage.tudelft.nl/11r49/documents/as98.pdf]
-<div class="mw-collapsible-content">
-<strong>Proof:</strong> █
-</div>
-</div>
 =References=
-[http://homepage.tudelft.nl/11r49/documents/as98.pdf]
+* {{BookReference|A Comprehensive Treatment of q-Calculus|2012|Thomas Ernst|prev=q-Sin|next=Q-derivative of q-Sine}}: (6.169)
 [[Category:SpecialFunction]]