Difference between revisions of "Delta derivative at right-scattered"
From timescalewiki
(Created page with "==Theorem== Let $\mathbb{T}$ be a time scale. Let $f \colon \mathbb{T} \rightarrow \mathbb{R}$ be continuous and right-scattered at $t \in \mathbb{T}$. Then $$f^{\...") |
(No difference)
|
Revision as of 05:16, 10 June 2016
Theorem
Let $\mathbb{T}$ be a time scale. Let $f \colon \mathbb{T} \rightarrow \mathbb{R}$ be continuous and right-scattered at $t \in \mathbb{T}$. Then $$f^{\Delta}(t)=\dfrac{f(\sigma(t))-f(t)}{\mu(t)},$$ where $f^{\Delta}$ denotes the delta derivative, $\sigma$ denotes the forward jump, and $\mu$ denotes the forward graininess.
