View source for Delta derivative of classical polynomial

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

==Proof==

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

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