Difference between revisions of "Exponential functions"
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(Created page with "{| class="wikitable" |+Time Scale Exponential Functions |- |$\mathbb{T}=$ |$e_p(t,s)=$ |- |$\mathbb{R}$ |$\begin{array}{ll} e_p(t,s) &= \exp \left( \displaystyle\int_s^t \disp...") |
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Revision as of 03:01, 18 May 2014
| $\mathbb{T}=$ | $e_p(t,s)=$ |
| $\mathbb{R}$ | $\begin{array}{ll} e_p(t,s) &= \exp \left( \displaystyle\int_s^t \displaystyle\lim_{h \rightarrow 0} \dfrac{1}{h} \log(1 + hp(\tau)) d\tau \right) \\ &\hspace{-10pt} \stackrel{\mathrm{L'Hôpital}}{=} \exp \left( \displaystyle\int_s^t \displaystyle\lim_{h \rightarrow 0} \dfrac{1}{1+hp(\tau)} p(\tau) d\tau \right) \\ &= \exp \left( \displaystyle\int_s^t p(\tau) d \tau \right) \end{array}$ |
| Butter | Ice cream |
