Arnol'd's analytic perturbation for the polar equation

Abstract

Based on the paper of Arnol'd [1] on the problems of Mathieu type, we suggest a modified Feynmann diagram technique to assist in solving problems of the form [see pdf for equation]. We then use this method to calculate eigenvalues and eigenfunctions to the polar problem, [see pdf for equation] with the quasiperiodic boundary condition on [0, 2p].