Difference between revisions of "Delta exponential with t=s"
From timescalewiki
(Created page with "<div class="toccolours mw-collapsible mw-collapsed" style="width:800px"> <strong>Theorem:</strong> Let $\mathbb{T}$ be a time scale, $t \in ...") |
|||
| Line 1: | Line 1: | ||
<div class="toccolours mw-collapsible mw-collapsed" style="width:800px"> | <div class="toccolours mw-collapsible mw-collapsed" style="width:800px"> | ||
| − | <strong>[[Delta exponential with t=s|Theorem]]:</strong> Let $\mathbb{T}$ be a [[time scale]], $t \in \mathbb{T}$, and $p \colon \mathbb{T} \rightarrow \mathbb{C}$ a [[regressive function]]. The following formula holds: | + | <strong>[[Delta exponential with t=s|Theorem]]:</strong> Let $\mathbb{T}$ be a [[time scale]], let $t \in \mathbb{T}$, and $p \colon \mathbb{T} \rightarrow \mathbb{C}$ a [[regressive function]]. The following formula holds: |
$$e_p(t,t;\mathbb{T})=1,$$ | $$e_p(t,t;\mathbb{T})=1,$$ | ||
where $e_p$ denotes the [[delta exponential]]. | where $e_p$ denotes the [[delta exponential]]. | ||
Revision as of 23:13, 31 May 2016
Theorem: Let $\mathbb{T}$ be a time scale, let $t \in \mathbb{T}$, and $p \colon \mathbb{T} \rightarrow \mathbb{C}$ a regressive function. The following formula holds: $$e_p(t,t;\mathbb{T})=1,$$ where $e_p$ denotes the delta exponential.
Proof: █
