Difference between revisions of "Derivative of alternative delta sine"

From timescalewiki
Jump to: navigation, search
(Created page with "<div class="toccolours mw-collapsible mw-collapsed" style="width:800px"> <strong>Theorem:</strong> Let $\mathbb{T}$ be a [[time scale]...")
 
 
Line 1: Line 1:
<div class="toccolours mw-collapsible mw-collapsed" style="width:800px">
+
==Theorem==
<strong>[[Derivative of alternative delta sine|Theorem]]:</strong> Let $\mathbb{T}$ be a [[time scale]]. The following formula holds:
+
Let $\mathbb{T}$ be a [[time scale]]. The following formula holds:
 
$$\mathrm{s}_{pq}^{\Delta}(t,s;\mathbb{T})=q(t)\mathrm{c}_{pq}(t,s;\mathbb{T})+p(t)\mathrm{s}_{pq}(t,s;\mathbb{T}),$$
 
$$\mathrm{s}_{pq}^{\Delta}(t,s;\mathbb{T})=q(t)\mathrm{c}_{pq}(t,s;\mathbb{T})+p(t)\mathrm{s}_{pq}(t,s;\mathbb{T}),$$
 
where $\mathrm{s}_{pq}$ denotes the [[delta spq|alternative delta sine]] and $\mathrm{c}_{pq}$ denotes the [[delta cpq|alternative delta cosine]].
 
where $\mathrm{s}_{pq}$ denotes the [[delta spq|alternative delta sine]] and $\mathrm{c}_{pq}$ denotes the [[delta cpq|alternative delta cosine]].
<div class="mw-collapsible-content">
+
 
<strong>Proof:</strong> █
+
==Proof==
</div>
+
 
</div>
+
==References==
 +
 
 +
[[Category:Theorem]]
 +
[[Category:Unproven]]

Latest revision as of 00:42, 15 September 2016

Theorem

Let $\mathbb{T}$ be a time scale. The following formula holds: $$\mathrm{s}_{pq}^{\Delta}(t,s;\mathbb{T})=q(t)\mathrm{c}_{pq}(t,s;\mathbb{T})+p(t)\mathrm{s}_{pq}(t,s;\mathbb{T}),$$ where $\mathrm{s}_{pq}$ denotes the alternative delta sine and $\mathrm{c}_{pq}$ denotes the alternative delta cosine.

Proof

References