Geodesic
The Dirichlet-type Laplace transforms
Caratelli, D.1 ; Pinelas, S.2 ; Ricci, P. E. 3
1 Electromagnetics Group, Department of Electrical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
2 Academia Militar-Departamento de Ciências Exatas e Engenharias, Av. Conde Castro Guimarães, 2720-113, Amadora, Portugal
3 Sezione di Matematica, International Telematic University UniNettuno, 39 Corso Vittorio Emanuele II, I-00186 Rome, Italy
Journal of nonlinear sciences and its applications, Tome 15 (2022) no. 3, p. 225-239.

Voir la notice de l'article provenant de la source International Scientific Research Publications

We show that it is possible to define extensions of the Laplace transform that use a general Dirichlet series as a kernel. These transforms, denoted by DLTs, further generalize those, considered in previous papers, in which the kernels were related to Laguerre-type exponentials or Bell polynomials. Computational techniques, exploiting expansions in Laguerre polynomials, and using Tricomi's method, have been considered. Since it turns out that the transforms considered are obtained as linear combinations of ordinary Laplace transforms, it is also possible to define an approximation of the relevant inverse transforms. Numerical experiments, performed with the algebra program Mathematica, show that the introduced technique is fast and efficient.
DOI : 10.22436/jnsa.015.03.05
Classification : 30B50, 44A10, 05A15, 05A40, 11B83
Keywords: General Dirichlet series, Laguerre-type exponentials, Bell polynomials, Laplace transform

Caratelli, D. 1 ; Pinelas, S. 2 ; Ricci, P. E.  3

1 Electromagnetics Group, Department of Electrical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
2 Academia Militar-Departamento de Ciências Exatas e Engenharias, Av. Conde Castro Guimarães, 2720-113, Amadora, Portugal
3 Sezione di Matematica, International Telematic University UniNettuno, 39 Corso Vittorio Emanuele II, I-00186 Rome, Italy 
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Caratelli, D.; Pinelas, S.; Ricci, P. E. . The Dirichlet-type Laplace transforms. Journal of nonlinear sciences and its applications, Tome 15 (2022) no. 3, p. 225-239. doi : 10.22436/jnsa.015.03.05. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.015.03.05/

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