Difference between revisions of "Zeros of delta gk"

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==Theorem==
<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 $0 \leq n \leq k-1$,
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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]].
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where $g_n$ denotes the [[delta gk|$g_k$ monomial]] and $\rho^k$ denotes [[composition|compositions]] of the [[backward jump]].
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<strong>Proof:</strong> █
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==Proof==
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==References==
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[[Category:Theorem]]
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[[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.

Proof

References