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The Bateman functions revisited after 90 years — a survey of old and new results
Please always quote using this URN: urn:nbn:de:bvb:20-opus-240970
- The Bateman functions and the allied Havelock functions were introduced as solutions of some problems in hydrodynamics about ninety years ago, but after a period of one or two decades they were practically neglected. In handbooks, the Bateman function is only mentioned as a particular case of the confluent hypergeometric function. In order to revive our knowledge on these functions, their basic properties (recurrence functional and differential relations, series, integrals and the Laplace transforms) are presented. Some new results are alsoThe Bateman functions and the allied Havelock functions were introduced as solutions of some problems in hydrodynamics about ninety years ago, but after a period of one or two decades they were practically neglected. In handbooks, the Bateman function is only mentioned as a particular case of the confluent hypergeometric function. In order to revive our knowledge on these functions, their basic properties (recurrence functional and differential relations, series, integrals and the Laplace transforms) are presented. Some new results are also included. Special attention is directed to the Bateman and Havelock functions with integer orders, to generalizations of these functions and to the Bateman-integral function known in the literature.…
Author: | Alexander Apelblat, Armando Consiglio, Francesco Mainardi |
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URN: | urn:nbn:de:bvb:20-opus-240970 |
Document Type: | Journal article |
Faculties: | Fakultät für Physik und Astronomie / Institut für Theoretische Physik und Astrophysik |
Language: | English |
Parent Title (English): | Mathematics |
ISSN: | 2227-7390 |
Year of Completion: | 2021 |
Volume: | 9 |
Issue: | 11 |
Article Number: | 1273 |
Source: | Mathematics (2021) 9:11, 1273. https://doi.org/10.3390/math9111273 |
DOI: | https://doi.org/10.3390/math9111273 |
Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik | |
Tag: | bateman functions; confluent hypergeometric functions; havelock functions; integral-bateman functions |
Release Date: | 2022/09/06 |
Date of first Publication: | 2021/06/01 |
Licence (German): | CC BY: Creative-Commons-Lizenz: Namensnennung 4.0 International |