Difference between revisions of "Product of delta exponentials with fixed t and s"
From timescalewiki
| Line 1: | Line 1: | ||
| − | + | ==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 function|regressive functions]]. The following formula holds: | |
$$e_p(t,s;\mathbb{T})e_q(t,s;\mathbb{T})=e_{p \oplus q}(t,s;\mathbb{T}),$$ | $$e_p(t,s;\mathbb{T})e_q(t,s;\mathbb{T})=e_{p \oplus q}(t,s;\mathbb{T}),$$ | ||
where $e_p$ denotes the [[delta exponential]] and $\oplus$ denotes [[circle plus]]. | where $e_p$ denotes the [[delta exponential]] and $\oplus$ denotes [[circle plus]]. | ||
| − | + | ||
| − | + | ==Proof== | |
| − | + | ||
| − | + | ==References== | |
| + | |||
| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Latest revision as of 22:21, 9 June 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: $$e_p(t,s;\mathbb{T})e_q(t,s;\mathbb{T})=e_{p \oplus q}(t,s;\mathbb{T}),$$ where $e_p$ denotes the delta exponential and $\oplus$ denotes circle plus.
