Difference between revisions of "Zeros of delta gk"
From timescalewiki
| Line 1: | Line 1: | ||
<div class="toccolours mw-collapsible mw-collapsed" style="width:800px"> | <div class="toccolours mw-collapsible mw-collapsed" style="width:800px"> | ||
| − | <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 $0 \leq n \leq k-1$, |
$$g_k(\rho^n(t),t)=0,$$ | $$g_k(\rho^n(t),t)=0,$$ | ||
| − | 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]]. |
<div class="mw-collapsible-content"> | <div class="mw-collapsible-content"> | ||
<strong>Proof:</strong> █ | <strong>Proof:</strong> █ | ||
</div> | </div> | ||
</div> | </div> | ||
Revision as of 20:06, 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 $g_k$ monomial and $\rho^k$ denotes compositions of the backward jump.
Proof: █
