Difference between revisions of "Delta sinh"
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Let $p$ and $-\mu p^2$ be [[regressive function|regressive functions]]. Then the $\Delta$ hyperbolic sine function is defined by | Let $p$ and $-\mu p^2$ be [[regressive function|regressive functions]]. Then the $\Delta$ hyperbolic sine function is defined by | ||
| − | $$\sinh_p(t,s) = \dfrac{e_p(t,s)-e_{-p}(t,s)}{ | + | $$\sinh_p(t,s) = \dfrac{e_p(t,s)-e_{-p}(t,s)}{2}.$$ |
| + | |||
| + | <div align="center"> | ||
| + | <gallery> | ||
| + | File:Integerdeltasinh,a=0.6,s=0plot.png|Graph of $\sinh_{0.6}(t,0;\mathbb{Z})$. | ||
| + | </gallery> | ||
| + | </div> | ||
=Properties= | =Properties= | ||
| − | + | [[Derivative of delta sinh]]<br /> | |
| − | + | [[Derivative of delta cosh]]<br /> | |
| − | + | [[Delta cosh minus delta sinh]]<br /> | |
| + | [[Delta hyperbolic trigonometric second order dynamic equation]]<br /> | ||
| − | + | <center>{{:Delta special functions footer}}</center> | |
| − | {{: | ||
| − | + | [[Category:specialfunction]] | |
| + | [[Category:Definition]] | ||
Latest revision as of 14:13, 28 January 2023
Let $p$ and $-\mu p^2$ be regressive functions. Then the $\Delta$ hyperbolic sine function is defined by $$\sinh_p(t,s) = \dfrac{e_p(t,s)-e_{-p}(t,s)}{2}.$$
Graph of $\sinh_{0.6}(t,0;\mathbb{Z})$.
Properties
Derivative of delta sinh
Derivative of delta cosh
Delta cosh minus delta sinh
Delta hyperbolic trigonometric second order dynamic equation
$\Delta$-special functions on time scales | ||||||
 $\cos_p$ |
 $\cosh_p$ |
 $e_p$ |
 $g_k$ |
 $h_k$ |
 $\sin_p$ |
 $\sinh_p$ |
