Nabla cosh

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

Properties[edit]

Dynamic equation for nabla cosh and nabla sinh

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

References[edit]

Nabla dynamic equations

$\nabla$-special functions on time scales

$\nabla$-$\widehat{\cos}_p$$\nabla$-$\widehat{\cosh}_p$$\nabla$-$\widehat{e}_p$$\nabla$-$h_k$$\nabla$-$g_k$$\nabla$-$\widehat{\sin}_p$$\nabla$-$\widehat{\sinh}_p$