The author considers the oblate spheroidal wave equation
where , and are given parameters. His aim is to derive asymptotic expansions for solutions of (*), which are uniformly valid for in certain subdomains of . To this end he assumes that remains fixed and lies in the interval (0,2), more precisely:
where is an arbitrary small constant. By applying three different Liouville transformations he obtains three types of expansions, which involve elementary, Airy and Bessel functions, respectively.