Eigenvalues Associated with Prolate Spheroidal Wave Functions of Zero Order

Abstract

Presented here are tables of values of X n and λ n , quantities defined by the eigenvalue problems $(1-x^2)\psi_n\Prime - 2x\psi_n\prime + (x_n - c^2x^2)\psi_n =0$ and $\lambda-n \psi_n (x) = \int_{-1}^1 {sin c(x-y)\over \pi(x-y)} \psi-n(y) dy.$ In addition, some approximations for these quantities are given and evaluated.