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

From timescalewiki
Jump to: navigation, search
Line 1: Line 1:
<div class="toccolours mw-collapsible mw-collapsed" style="width:800px">
+
==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:
<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]].
<div class="mw-collapsible-content">
+
 
<strong>Proof:</strong>  █
+
==Proof==
</div>
+
 
</div>
+
==References==
 +
 
 +
[[Category:Theorem]]
 +
[[Category:Unproven]]

Revision as of 01:59, 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 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