Latest revision as of 23:38, 11 December 2016

$$\widehat{\cosh}_p(t,s)=\dfrac{\widehat{e}_p(t,s)+\widehat{e}_{-p}(t,s)}{2}$$

Properties

$\widehat{\cosh}_p^{\nabla}(t,s)=p(t)\widehat{\sinh}_p(t,s)$, where $\widehat{\sinh}$ is the $\nabla$-$\sinh$ function.
$\widehat{\cosh}^2_p(t,s)-\widehat{\sinh}^2_p(t,s)=\widehat{e}_{\nu p^2}(t,s)$
$\widehat{\cosh}_p(t,s) + \widehat{\sinh}_p(t,s)=\hat{e}_p(t,s)$
$\widehat{\cosh}_p(t,s)-\widehat{\sinh}_p(t,s)=\widehat{e}_{-p}(t,s)$

$\nabla$-$\widehat{\cosh}_p$

$\nabla$-$\widehat{e}_p$

@@ Line 1: / Line 1: @@
-$$\hat{\cosh}_p(t,s)=\dfrac{\hat{e}_p(t,s)+\hat{e}_{-p}(t,s)}{2}$$
+$$\widehat{\cosh}_p(t,s)=\dfrac{\widehat{e}_p(t,s)+\widehat{e}_{-p}(t,s)}{2}$$
 =Properties=
-<div class="toccolours mw-collapsible mw-collapsed" style="width:800px">
+[[Dynamic equation for nabla cosh and nabla sinh]]<br />
-<strong>Theorem:</strong> If $\alpha > 0$ with $\alpha^2\nu \in \mathcal{\nu}$, a [[regressive function]], then $\hat{\cosh}_{\gamma}(\cdot,s)$ and $\hat{\sinh}_{\gamma}(\cdot,s)$ solve the $\nabla$ dynamic equation
-$$y^{\nabla \nabla}-\gamma^2 y=0.$$
-<div class="mw-collapsible-content">
-<strong>Proof:</strong> proof goes here █
-</div>
-</div>
-#$\hat{\cosh}_p^{\nabla}(t,s)=p(t)\hat{\sinh}_p(t,s)$, where $\hat{\sinh}$ is the [[Nabla sinh|$\nabla$-$\sinh$]] function.
+#$\widehat{\cosh}_p^{\nabla}(t,s)=p(t)\widehat{\sinh}_p(t,s)$, where $\widehat{\sinh}$ is the [[Nabla sinh|$\nabla$-$\sinh$]] function.
-#$\hat{\cosh}^2_p(t,s)-\hat{\sinh}^2_p(t,s)=\hat{e}_{\nu p^2}(t,s)$
+#$\widehat{\cosh}^2_p(t,s)-\widehat{\sinh}^2_p(t,s)=\widehat{e}_{\nu p^2}(t,s)$
-#$\hat{\cosh}_p(t,s)-\hat{\sinh}_p(t,s)=\hat{e}_{-p}(t,s)$
+#$\widehat{\cosh}_p(t,s) + \widehat{\sinh}_p(t,s)=\hat{e}_p(t,s)$
+#$\widehat{\cosh}_p(t,s)-\widehat{\sinh}_p(t,s)=\widehat{e}_{-p}(t,s)$
 =References=
 [http://faculty.cord.edu/andersod/p20.pdf Nabla dynamic equations]
+{{:Nabla special functions footer}}