New Investigation on the Spheroidal Wave Equations

Abstract

Changing the spheroidal wave equations into new Schro$dinger's form, the super-potential expanded in the series form of the parameter $\alpha$are obtained in the paper. This general form of the super-potential makes it easy to get the ground eigenfunctions of the spheroidal equations. But the shape-invariance property is not retained and the corresponding recurrence relations of the form (4) could not be extended from the associated Legendre functions to the case of the spheroidal functions.