On the Asymptotics of Eigenvalues of the Spin-Weighted Spheroidal Equation

Abstract

Solutions of the spin-weighted spheroidal differential equation are presented in the form of the series involving confluent hypergeometric functions. Relations between solutions with different domains of convergence are derived by considering the confluence of two singularities in an auxiliary equation with four regular singularities. These relations are used to obtain exponentially small corrections to asymptotic expansion of eigenvalues.