Eigenvalues Associated with Prolate Spheroidal Wave Functions of Zero Order

Presented here are tables of values of x,, and A,, , quantities defined by the eigenvalue problems (1 aiid X2)W 2xpn + (Xn c V ) ^ = 0 M) = f J-i sin;fa " ir(x -- y) Uy)dy. In addition, some approximations for these quantities are given and evaluated. The prolate spheroidal wave functions of zero order, pn (x), n = 0, 1, · · · , are bounded continuous solutions of both the differential equation dx1 and the integral equation KUX) dx = f s i '7ix-fuy)dy.