The Laplace Transform of Composed Functions and Bivariate Bell Polynomials
The problem of computing the Laplace transform of composed functions has not found its way into the literature because it was customarily believed that there were no suitable formula to solve it. Actually, it has been shown in previous work that by making use of Bell polynomials, efficient approxima...
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| Format: | Article |
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MDPI AG
2022-10-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/11/11/591 |
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| author | Diego Caratelli Rekha Srivastava Paolo Emilio Ricci |
| author_facet | Diego Caratelli Rekha Srivastava Paolo Emilio Ricci |
| author_sort | Diego Caratelli |
| collection | DOAJ |
| description | The problem of computing the Laplace transform of composed functions has not found its way into the literature because it was customarily believed that there were no suitable formula to solve it. Actually, it has been shown in previous work that by making use of Bell polynomials, efficient approximations can be found. Moreover, using an extension of Bell’s polynomials to bivariate functions, it is also possible to approximate the Laplace transform of composed functions of two variables. This topic is solved in this paper and some numerical verifications, due to the first author using the computer algebra system Mathematica<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mi mathvariant="sans-serif">©</mi></msup></semantics></math></inline-formula>, are given proving the effectiveness of the proposed method. |
| first_indexed | 2024-03-09T19:16:10Z |
| format | Article |
| id | doaj.art-72dced41d5834ed883b57848c4dd4b47 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-09T19:16:10Z |
| publishDate | 2022-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-72dced41d5834ed883b57848c4dd4b472023-11-24T03:43:57ZengMDPI AGAxioms2075-16802022-10-01111159110.3390/axioms11110591The Laplace Transform of Composed Functions and Bivariate Bell PolynomialsDiego Caratelli0Rekha Srivastava1Paolo Emilio Ricci2Department of Electrical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The NetherlandsDepartment of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, CanadaDepartment of Mathematics, International Telematic University UniNettuno, Corso Vittorio Emanuele II, 39, 00186 Rome, ItalyThe problem of computing the Laplace transform of composed functions has not found its way into the literature because it was customarily believed that there were no suitable formula to solve it. Actually, it has been shown in previous work that by making use of Bell polynomials, efficient approximations can be found. Moreover, using an extension of Bell’s polynomials to bivariate functions, it is also possible to approximate the Laplace transform of composed functions of two variables. This topic is solved in this paper and some numerical verifications, due to the first author using the computer algebra system Mathematica<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mi mathvariant="sans-serif">©</mi></msup></semantics></math></inline-formula>, are given proving the effectiveness of the proposed method.https://www.mdpi.com/2075-1680/11/11/591Laplace transform of composed functionsbivariate Bell polynomials |
| spellingShingle | Diego Caratelli Rekha Srivastava Paolo Emilio Ricci The Laplace Transform of Composed Functions and Bivariate Bell Polynomials Axioms Laplace transform of composed functions bivariate Bell polynomials |
| title | The Laplace Transform of Composed Functions and Bivariate Bell Polynomials |
| title_full | The Laplace Transform of Composed Functions and Bivariate Bell Polynomials |
| title_fullStr | The Laplace Transform of Composed Functions and Bivariate Bell Polynomials |
| title_full_unstemmed | The Laplace Transform of Composed Functions and Bivariate Bell Polynomials |
| title_short | The Laplace Transform of Composed Functions and Bivariate Bell Polynomials |
| title_sort | laplace transform of composed functions and bivariate bell polynomials |
| topic | Laplace transform of composed functions bivariate Bell polynomials |
| url | https://www.mdpi.com/2075-1680/11/11/591 |
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