Estimates of spheroidal functions (Q1803138)

A detailed investigation of the maxima of various classes of spheroidal wave functions (found by separation of variables in the Helmholtz equation) is given. The basis of all are theorems due to Sonine and Hardy: the maxima of solutions to ordinary differential equations in \([0,1]\) are located near the zeros or the maxima of the coefficients (or in the endpoints 0,1). This is specified here to the wave functions under consideration, but moreover the author deals with a thorough analysis of estimates of those functions, especially the relations between successive maxima.