# Delta derivative of classical polynomial

From timescalewiki

## 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

- Martin Bohner and Allan Peterson:
*Dynamic Equations on Time Scales*(2001)... (previous)... (next): Theorem 1.24(i)