The Bateman Functions Revisited after 90 Years—A Survey of Old and New Results

Alexander Apelblat, Armando Consiglio and Francesco Mainardi
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Alexander Apelblat: Department of Chemical Engineering, Ben Gurion University of the Negev, Beer Sheva 84105, Israel
Armando Consiglio: Institut für Theoretische Physik und Astrophysik and Würzburg-Dresden Cluster of Excellence ct.qmat, Universität Würzburg, D-97074 Würzburg, Germany
Francesco Mainardi: Dipartimento di Fisica e Astronomia, Università di Bologna, & INFN, Via Irnerio 46, I-40126 Bologna, Italy

Mathematics, 2021, vol. 9, issue 11, 1-27

Abstract: 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 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.

Keywords: bateman functions; havelock functions; integral-bateman functions; confluent hypergeometric functions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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