Difference between revisions of "Relationship between delta hk and delta gk"

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==Theorem==
<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:
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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 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]].
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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 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.

Proof

References