Nabla cosh

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

Properties

Second order dynamic equation for nabla cosh

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

Nabla dynamic equations

$\nabla$-special functions on time scales

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