Difference between revisions of "Semigroup property of delta exponential"
From timescalewiki
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| − | + | ==Theorem== | |
| − | + | Let $\mathbb{T}$ be a [[time scale]], let $t,s \in \mathbb{T}$, and let $p \in \mathcal{R}\left( \mathbb{T},\mathbb{C} \right)$ be a [[regressive function]]. The following formula holds: | |
$$e_p(t,r;\mathbb{T})e_p(r,s;\mathbb{T})=e_p(t,s;\mathbb{T}),$$ | $$e_p(t,r;\mathbb{T})e_p(r,s;\mathbb{T})=e_p(t,s;\mathbb{T}),$$ | ||
where $e_p$ denotes the [[delta exponential]]. | where $e_p$ denotes the [[delta exponential]]. | ||
| − | + | ||
| − | + | ==Proof== | |
| − | + | ||
| − | + | ==References== | |
| + | |||
| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Revision as of 21:31, 9 June 2016
Theorem
Let $\mathbb{T}$ be a time scale, let $t,s \in \mathbb{T}$, and let $p \in \mathcal{R}\left( \mathbb{T},\mathbb{C} \right)$ be a regressive function. The following formula holds: $$e_p(t,r;\mathbb{T})e_p(r,s;\mathbb{T})=e_p(t,s;\mathbb{T}),$$ where $e_p$ denotes the delta exponential.
