Difference between revisions of "Gaussian bell"
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(Created page with "The Gaussian bell is defined<ref name=gaussbell /> ==References== <references> <ref name=gaussbell>[http://www.math.unl.edu/~apeterson1/pub/epsgauss.pdf Erbe, L.; Peterson, A...") |
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| − | The Gaussian bell is defined<ref name=gaussbell /> | + | Let $\mathbb{T}$ be a [[time_scale | time scale]] with $0 \in \mathbb{T}$. Let $p \colon \mathbb{T} \rightarrow \mathbb{R}$ be [[regressive_function | regressive]] and defined by |
| + | $$p(t)=\ominus(t \odot 1).$$ | ||
| + | The Gaussian bell $\mathbf{E} \colon \mathbb{T} \rightarrow \mathbb{R}$ is defined<ref name=gaussbell /> to be the [[exponential_function | exponential function]] | ||
| + | $$\mathbf{E}(t)=e_{p}(t,0).$$ | ||
==References== | ==References== | ||
Revision as of 02:24, 26 May 2014
Let $\mathbb{T}$ be a time scale with $0 \in \mathbb{T}$. Let $p \colon \mathbb{T} \rightarrow \mathbb{R}$ be regressive and defined by $$p(t)=\ominus(t \odot 1).$$ The Gaussian bell $\mathbf{E} \colon \mathbb{T} \rightarrow \mathbb{R}$ is defined<ref name=gaussbell /> to be the exponential function $$\mathbf{E}(t)=e_{p}(t,0).$$
References
<references> <ref name=gaussbell>Erbe, L.; Peterson, A.;Simon, M. Square integrability of Gaussian bells on time scales. Comput. Math. Appl. 49 (2005), no. 5-6, 871--883. </ref> </references>
