Difference between revisions of "Zeros of delta gk"
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(Created page with "<div class="toccolours mw-collapsible mw-collapsed" style="width:800px"> <strong>Theorem:</strong> Let $\mathbb{T}$ be a time scale, let $t,s \in \mathbb...") |
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| − | + | ==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,$$ |
| − | where $g_n$ denotes the [[delta gk]] and $\rho^k$ denotes [[composition|compositions]] of the [[backward jump]]. | + | where $g_n$ denotes the [[delta gk|$g_k$ monomial]] and $\rho^k$ denotes [[composition|compositions]] of the [[backward jump]]. |
| − | + | ||
| − | + | ==Proof== | |
| − | + | ||
| − | + | ==References== | |
| + | |||
| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Latest revision as of 01:58, 10 June 2016
Theorem
Let $\mathbb{T}$ be a time scale, let $t,s \in \mathbb{T}$, and let $k$ be a nonnegative integer. Then for all $0 \leq n \leq k-1$, $$g_k(\rho^n(t),t)=0,$$ where $g_n$ denotes the $g_k$ monomial and $\rho^k$ denotes compositions of the backward jump.
