View source for Delta derivative of reciprocal of classical polynomial

==Theorem==
Let $\mathbb{T}$ be a [[time scale]], let $\alpha$ a constant, let $m \in \mathbb{N}$, and define $g\colon \mathbb{T} \rightarrow \mathbb{R}$ by $g(t)=\dfrac{1}{(t-\alpha)^m}$. Then
$$g^{\Delta}(t)=-\displaystyle\sum_{j=0}^{m-1} \dfrac{1}{(\sigma(t)-\alpha)^{m-j}(t-\alpha)^{j+1}},$$
where $\sigma$ denotes the [[forward jump]].
==Proof==

==References==
* {{BookReference|Dynamic Equations on Time Scales|2001|Martin Bohner|author2=Allan Peterson|prev=Delta derivative of classical polynomial|next=findme}}: Theorem $1.24(ii)$

[[Category:Theorem]]
[[Category:Unproven]]