Difference between revisions of "Product of delta exponentials with fixed t and s"
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<strong>[[Product of delta exponentials with fixed t and s|Theorem]]:</strong> Let $\mathbb{T}$ be a [[time scale]], $t,s \in \mathbb{T}$, and let $p,q \in \mathcal{R}\left(\mathbb{T},\mathbb{C}\right)$ be [[regressive function|regressive functions]]. The following formula holds: | <strong>[[Product of delta exponentials with fixed t and s|Theorem]]:</strong> Let $\mathbb{T}$ be a [[time scale]], $t,s \in \mathbb{T}$, and let $p,q \in \mathcal{R}\left(\mathbb{T},\mathbb{C}\right)$ be [[regressive function|regressive functions]]. The following formula holds: | ||
$$e_p(t,s)e_q(t,s)=e_{p \oplus q}(t,s),$$ | $$e_p(t,s)e_q(t,s)=e_{p \oplus q}(t,s),$$ | ||
− | where $e_p$ denotes the [[delta exponential]] and $\oplus$ denotes | + | where $e_p$ denotes the [[delta exponential]] and $\oplus$ denotes [[circle plus]]. |
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<strong>Proof:</strong> █ | <strong>Proof:</strong> █ | ||
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</div> | </div> |
Revision as of 23:09, 31 May 2016
Theorem: Let $\mathbb{T}$ be a time scale, $t,s \in \mathbb{T}$, and let $p,q \in \mathcal{R}\left(\mathbb{T},\mathbb{C}\right)$ be regressive functions. The following formula holds: $$e_p(t,s)e_q(t,s)=e_{p \oplus q}(t,s),$$ where $e_p$ denotes the delta exponential and $\oplus$ denotes circle plus.
Proof: █