Difference between revisions of "Relationship between delta hk and 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 $t,s \in \mathbb{T}$, and let $k$ ...") |
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| − | <strong>Theorem:</strong> Let $\mathbb{T}$ be a [[time scale]], let $t,s \in \mathbb{T}$, and let $k$ be a nonnegative integer. Then the following formula holds: | + | <strong>[[Relationship between delta hk and 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 the following formula holds: |
$$h_k(t,s;\mathbb{T})=(-1)^kg_k(s,t;\mathbb{T}),$$ | $$h_k(t,s;\mathbb{T})=(-1)^kg_k(s,t;\mathbb{T}),$$ | ||
where $h_k$ denotes the [[delta hk]] and $g_k$ denotes the [[delta gk]]. | where $h_k$ denotes the [[delta hk]] and $g_k$ denotes the [[delta gk]]. | ||
Revision as of 20:10, 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 the following formula holds: $$h_k(t,s;\mathbb{T})=(-1)^kg_k(s,t;\mathbb{T}),$$ where $h_k$ denotes the delta hk and $g_k$ denotes the delta gk.
Proof: █
