Difference between revisions of "Derivative of alternative delta sine"
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| − | + | ==Theorem== | |
| − | + | Let $\mathbb{T}$ be a [[time scale]]. The following formula holds: | |
$$\mathrm{s}_{pq}^{\Delta}(t,s;\mathbb{T})=q(t)\mathrm{c}_{pq}(t,s;\mathbb{T})+p(t)\mathrm{s}_{pq}(t,s;\mathbb{T}),$$ | $$\mathrm{s}_{pq}^{\Delta}(t,s;\mathbb{T})=q(t)\mathrm{c}_{pq}(t,s;\mathbb{T})+p(t)\mathrm{s}_{pq}(t,s;\mathbb{T}),$$ | ||
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]]. | ||
| − | + | ||
| − | + | ==Proof== | |
| − | + | ||
| − | + | ==References== | |
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| + | [[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.
