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Generalized elementary functions |
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| Authors: | Giselle Antunes Monteiro Antonín Slavík |
| Institution: | 1. Mathematical Institute, Academy of Sciences of the Czech Republic, ?itná 25, 115 67 Praha 1, Czech Republic;2. Charles University in Prague, Faculty of Mathematics and Physics, Sokolovská 83, 186 75 Praha 8, Czech Republic |
| Abstract: | We use the theory of generalized linear differential equations to introduce new definitions of the exponential, hyperbolic and trigonometric functions. We derive some basic properties of these generalized functions, and show that the time scale elementary functions with Lebesgue integrable arguments represent a special case of our definitions. |
| Keywords: | Elementary functions Kurzweil&ndash Stieltjes integral Generalized linear ordinary differential equations Time scale calculus |
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