  The perturbation method in supersymmetric quantum mechanics (SUSYQM) is used
to study the spheroidal wave functions' recurrence relations, which are
revealed by the shape-invariance property of the super-potential. The
super-potential is expanded by the parameter alpha and could be gotten by
approximation method. Up to the first order, it has the shape-invariance
property and the excited spheroidal wave functions are gotten. Also, all the
first term eigenfunctions obtained are in closed form. They are advantageous to
investigating for involved physical problems of spheroidal wave function.
