Ground State Eigenfunction of Spheroidal Wave Functions

We study the spin-weighted spheroidal wave functions in the case of s=m=0. Their eigenvalue problem is investigated by the perturbation method in supersymmetric quantum mechanics. In the first three terms of parameter α=a²w², the ground eigenvalue and eigenfunction are obtained. The obtained ground eigenfunction is elegantly in closed forms. These results are new and very useful for the application of the spheroidal wave functions.