Difference between revisions of "Quotient of delta exponentials with fixed t and s"
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<strong>[[Quotient of delta exponentials with fixed t and s|Theorem]]:</strong> Let $\mathbb{T}$ be a [[time scale]], $t,s \in \mathbb{T}$, and let $p,q \in \mathcal{R}(\mathbb{T},\mathbb{C})$. The following formula holds: | <strong>[[Quotient of delta exponentials with fixed t and s|Theorem]]:</strong> Let $\mathbb{T}$ be a [[time scale]], $t,s \in \mathbb{T}$, and let $p,q \in \mathcal{R}(\mathbb{T},\mathbb{C})$. The following formula holds: | ||
| − | $$\dfrac{e_p(t,s)}{e_q(t,s)} = e_{p \ominus q}(t,s),$$ | + | $$\dfrac{e_p(t,s;\mathbb{T})}{e_q(t,s;\mathbb{T})} = e_{p \ominus q}(t,s;\mathbb{T}),$$ |
where $e_p$ denotes the [[delta exponential]] and $\ominus$ denotes [[circle minus]]. | where $e_p$ denotes the [[delta exponential]] and $\ominus$ denotes [[circle minus]]. | ||
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Revision as of 23:20, 31 May 2016
Theorem: Let $\mathbb{T}$ be a time scale, $t,s \in \mathbb{T}$, and let $p,q \in \mathcal{R}(\mathbb{T},\mathbb{C})$. The following formula holds: $$\dfrac{e_p(t,s;\mathbb{T})}{e_q(t,s;\mathbb{T})} = e_{p \ominus q}(t,s;\mathbb{T}),$$ where $e_p$ denotes the delta exponential and $\ominus$ denotes circle minus.
Proof: █
