Difference between revisions of "Zeros of delta gk"
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<strong>[[Zeros of delta gk|Theorem]]:</strong> Let $\mathbb{T}$ be a time scale, let $t,s \in \mathbb{T}$, and let $k$ be a nonnegative integer. Then for all $0 \leq n \leq k-1$, | <strong>[[Zeros of delta gk|Theorem]]:</strong> Let $\mathbb{T}$ be a time scale, let $t,s \in \mathbb{T}$, and let $k$ be a nonnegative integer. Then for all $0 \leq n \leq k-1$, | ||
| − | $$ | + | $$g_k(\rho^n(t),t)=0,$$ |
where $g_n$ denotes the [[delta gk]] and $\rho^k$ denotes [[composition|compositions]] of the [[backward jump]]. | where $g_n$ denotes the [[delta gk]] and $\rho^k$ denotes [[composition|compositions]] of the [[backward jump]]. | ||
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Revision as of 20:05, 1 June 2016
Theorem: Let $\mathbb{T}$ be a time scale, let $t,s \in \mathbb{T}$, and let $k$ be a nonnegative integer. Then for all $0 \leq n \leq k-1$, $$g_k(\rho^n(t),t)=0,$$ where $g_n$ denotes the delta gk and $\rho^k$ denotes compositions of the backward jump.
Proof: █
