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
 
$$\sinh_p(t,s) = \dfrac{e_p(t,s)-e_{-p}(t,s)}{2}.$$
 
$$\sinh_p(t,s) = \dfrac{e_p(t,s)-e_{-p}(t,s)}{2}.$$
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<div align="center">
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<gallery>
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File:Integerdeltasinh,a=0.6,s=0plot.png|Graph of $\sinh_{0.6}(t,0;\mathbb{Z})$.
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</gallery>
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</div>
  
 
=Properties=
 
=Properties=
{{:Derivative of delta sinh}}
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[[Derivative of delta sinh]]<br />
{{:Delta cosh minus delta sinh}}
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[[Derivative of delta cosh]]<br />
{{:Delta hyperbolic trigonometric second order dynamic equation}}
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[[Delta cosh minus delta sinh]]<br />
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[[Delta hyperbolic trigonometric second order dynamic equation]]<br />
  
=Relation to other functions=
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<center>{{:Delta special functions footer}}</center>
{{:Derivative of delta cosh}}
 
  
{{:Delta special functions footer}}
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[[Category:specialfunction]]
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[[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 $$\sinh_p(t,s) = \dfrac{e_p(t,s)-e_{-p}(t,s)}{2}.$$

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


$\cos_p$

$\cosh_p$

$e_p$

$g_k$

$h_k$

$\sin_p$

$\sinh_p$