The generalized epsilon function : an alternative to the exponential function

Jónás Tamás: The generalized epsilon function : an alternative to the exponential function. In: Acta cybernetica, (25) 3. pp. 703-716. (2022)

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Abstract

It is well known that the exponential function plays an extremely important role in many areas of science. In this study, a generator function-based mapping, called the generalized epsilon function is presented. Next, we demonstrate that the exponential function is an asymptotic generalized epsilon function. Exploiting this result and the fact that this new function is generator function-dependent, it can be utilized as a very flexible alternative to the exponential function in a wide range of applications. We should add that if the generator is a rational function, then the generalized epsilon function is rational as well. In this case, the generalized epsilon function is computationally simple and it may be treated as an easy-to-compute alternative to the exponential function. In this paper, we briefly present two applications of this novel function: an approximation to the exponential probability distribution, and an alternative to the sigmoid function on a bounded domain.

Item Type: Article
Journal or Publication Title: Acta cybernetica
Date: 2022
Volume: 25
Number: 3
ISSN: 0324-721X
Page Range: pp. 703-716
Language: English
Publisher: University of Szeged, Institute of Informatics
Place of Publication: Szeged
Event Title: Conference of PhD Students in Computer Science (12.) (2020) (Szeged)
Related URLs: http://acta.bibl.u-szeged.hu/75566/
DOI: 10.14232/actacyb.294699
Uncontrolled Keywords: Exponenciális függvény
Additional Information: Bibliogr.: p. 715-716. ; összefoglalás angol nyelven
Subjects: 01. Natural sciences
01. Natural sciences > 01.01. Mathematics
01. Natural sciences > 01.02. Computer and information sciences
Date Deposited: 2022. May. 13. 10:16
Last Modified: 2022. May. 13. 10:16
URI: http://acta.bibl.u-szeged.hu/id/eprint/75630

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