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Proceedings of the 1st International Symposium on Square Bamboos and the Geometree (ISSBG 2022)

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Laplace Transform Approximation of Nested Functions Using Bell’s Polynomials
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Authors
Paolo Emilio Ricci1, *, Diego Caratelli2, 3, Sandra Pinelas3, 4
1
UniNettuno International Telematic University, Rome, Italy
2
Department of Electrical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands
3
Department of Research and Development, The Antenna Company, Eindhoven, The Netherlands
4
Department of Exact Sciences and Engineering, Portuguese Military Academy, Amadora, Portugal
*
Corresponding author. Email: paoloemilioricci@gmail.com
Corresponding Author
Paolo Emilio Ricci
Article History
Received 10 January 2023
Revised 28 February 2023
Accepted 23 October 2023
Available Online 29 November 2023
DOI
https://doi.org/10.55060/s.atmps.231115.006
Keywords
Laplace Transform
Bell’s polynomials
Composed functions
Abstract

Bell’s polynomials have been used in many different fields, ranging from number theory to operator theory. In this article we show a method to compute the Laplace Transform (LT) of nested analytic functions. To this aim, we provide a table of the first few values of the complete Bell’s polynomials, which are then used to evaluate the LT of composed exponential functions. Furthermore, a code for approximating the LT of general analytic composed functions is created and presented. A graphical verification of the proposed technique is illustrated in the last section.

Copyright
© 2023 The Authors. Published by Athena International Publishing B.V.
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (https://creativecommons.org/licenses/by-nc/4.0/).
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Cite This Article

ris 
TY  - CONF
AU  - Paolo Emilio Ricci
AU  - Diego Caratelli
AU  - Sandra Pinelas
PY  - 2023
DA  - 2023/11/29
TI  - Laplace Transform Approximation of Nested Functions Using Bell’s Polynomials
BT  - Proceedings of the 1st International Symposium on Square Bamboos and the Geometree (ISSBG 2022)
PB  - Athena Publishing
SP  - 55
EP  - 70
SN  - 2949-9429
UR  - https://doi.org/10.55060/s.atmps.231115.006
DO  - https://doi.org/10.55060/s.atmps.231115.006
ID  - Ricci2023
ER  -
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