Difference between revisions of "Relationship between delta hk and delta gk"
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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 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]]. | ||
| − | + | ||
| − | + | ==Proof== | |
| − | + | ||
| − | + | ==References== | |
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| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Latest revision as of 15:40, 22 September 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.
