Difference between revisions of "Reciprocal of delta exponential"

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==Theorem==
<strong>[[Reciprocal of delta exponential|Theorem]]:</strong> Let $\mathbb{T}$ be a [[time scale]], let $t,s \in \mathbb{T}$, and let $p \in \mathcal{R}(\mathbb{T},\mathbb{C})$ be a [[regressive function]]. The following formula holds:
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Let $\mathbb{T}$ be a [[time scale]], let $t,s \in \mathbb{T}$, and let $p \in \mathcal{R}(\mathbb{T},\mathbb{C})$ be a [[regressive function]]. The following formula holds:
 
$$\dfrac{1}{e_p(t,s;\mathbb{T})}=e_{\ominus p}(s,t;\mathbb{T}),$$
 
$$\dfrac{1}{e_p(t,s;\mathbb{T})}=e_{\ominus p}(s,t;\mathbb{T}),$$
 
where $e_p$ denotes the [[delta exponential]] and $\ominus$ denotes [[circle minus]].
 
where $e_p$ denotes the [[delta exponential]] and $\ominus$ denotes [[circle minus]].
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<strong>Proof:</strong>  █
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==Proof==
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==References==
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[[Category:Theorem]]
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[[Category:Unproven]]

Latest revision as of 22:20, 9 June 2016

Theorem

Let $\mathbb{T}$ be a time scale, let $t,s \in \mathbb{T}$, and let $p \in \mathcal{R}(\mathbb{T},\mathbb{C})$ be a regressive function. The following formula holds: $$\dfrac{1}{e_p(t,s;\mathbb{T})}=e_{\ominus p}(s,t;\mathbb{T}),$$ where $e_p$ denotes the delta exponential and $\ominus$ denotes circle minus.

Proof

References