Stokes multipliers for asymptotic solutions of a certain differential equation

Abstract

Series (2) converge for I x| < oo and are useful for computing the yj's when x is small. When x is large, convergence is slow and it is more advantageous to use asymptotic expansions. If we let x = rei0 and divide the x-plane into 2p sectors by the radial lines 6=7rh/p; h=O, 1, * , 2p-1, then, as Trjitzinsky [8](1) has shown, there is associated with each of these sectors n independent solutions y,(x) of (1) such that y,(x)-A,(x) where the asymptotic forms