  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 known in the literature generalizations of
these functions and to the Bateman-integral function.
