The Stokes phenomenon and certain nth-order differential equations II. The Stokes phenomenon

Introduction . In paper I(2), solutions have been found for the n th-order differential equations (I, 3), (I, 9), (I, 18), namely, where ϑ = wd / dw , m is any rational fraction and a any constant. Power-series solutions have been found for these equations, together with integral representations and their asymptotic expressions valid for restricted ranges of arg z . The object of this second paper is to consider these asymptotic solutions in more detail, and to extend these expressions to all values of arg z . The Stokes phenomenon will be manifest throughout, and this will be treated in a manner suitable for further application.