Difference between revisions of "Product of delta exponentials with fixed t and s"

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(Created page with "<div class="toccolours mw-collapsible mw-collapsed" style="width:800px"> <strong>Theorem:</strong> Let $\mathbb{T}$ be a [...")
 
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<strong>[[Product of delta exponentials with fixed t and s|Theorem]]:</strong> Let $\mathbb{T}$ be a [[time scale]], $t,s \in \mathbb{T}$, and let $p,q \in \mathcal{R}\left(\mathbb{T},\mathbb{C}\right)$ be [[regressive function|regressive functions]]. The following formula holds:
 
<strong>[[Product of delta exponentials with fixed t and s|Theorem]]:</strong> Let $\mathbb{T}$ be a [[time scale]], $t,s \in \mathbb{T}$, and let $p,q \in \mathcal{R}\left(\mathbb{T},\mathbb{C}\right)$ be [[regressive function|regressive functions]]. The following formula holds:
 
$$e_p(t,s)e_q(t,s)=e_{p \oplus q}(t,s),$$
 
$$e_p(t,s)e_q(t,s)=e_{p \oplus q}(t,s),$$
where $e_p$ denotes the [[delta exponential]] and $\oplus$ denotes the [[circle plus]].
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where $e_p$ denotes the [[delta exponential]] and $\oplus$ denotes [[circle plus]].
 
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<strong>Proof:</strong>  █  
 
<strong>Proof:</strong>  █  
 
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Revision as of 23:09, 31 May 2016

Theorem: Let $\mathbb{T}$ be a time scale, $t,s \in \mathbb{T}$, and let $p,q \in \mathcal{R}\left(\mathbb{T},\mathbb{C}\right)$ be regressive functions. The following formula holds: $$e_p(t,s)e_q(t,s)=e_{p \oplus q}(t,s),$$ where $e_p$ denotes the delta exponential and $\oplus$ denotes circle plus.

Proof: