# Difference between revisions of "Delta derivative of classical polynomial"

From timescalewiki

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==References== | ==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) | * {{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) | ||

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+ | [[Category:Theorem]] | ||

+ | [[Category:Unproven]] |

## Revision as of 15:05, 25 September 2016

## 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)