Difference between revisions of "Reciprocal of delta exponential"
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<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: | <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: | ||
| − | $$\dfrac{1}{e_p(t,s)}=e_{\ominus p}(s,t),$$ | + | $$\dfrac{1}{e_p(t,s;\mathbb{T})}=e_{\ominus p}(s,t;\mathbb{T}),$$ |
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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Revision as of 23:19, 31 May 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: █
