TY  - JOUR
A1  - Apelblat, Alexander
A1  - Consiglio, Armando
A1  - Mainardi, Francesco
T1  - The Bateman functions revisited after 90 years — a survey of old and new results
T2  - Mathematics
N2  - 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.
KW  - bateman functions
KW  - havelock functions
KW  - integral-bateman functions
KW  - confluent hypergeometric functions
Y1  - 2021
UR  - https://opus.bibliothek.uni-wuerzburg.de/frontdoor/index/index/docId/24097
UR  - https://nbn-resolving.org/urn:nbn:de:bvb:20-opus-240970
SN  - 2227-7390
VL  - 9
IS  - 11
ER  -