Difference between revisions of "Delta derivative of classical polynomial"

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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]]
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[[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