Global Analysis in Linear Differential Equations

This book treats several topics on the global analysis of linear differential equations in the complex domain, using original methods of analysis developed by K. Okubo and the present author. For example, global analysis of linear differential equations is closely related to that of linear difference equations. Through the asymptotic behaviour of solutions of linear difference equations, connection problems for hypergeometric systems can be solved, i.e. Fuchsian differential equations and Stokes phenomenon for Birkhoff systems. Furthermore, the calculation of monodromy groups is explained in detail. Audience: This volume will be of interest to researchers and graduate students whose work involves ordinary differential equations, special functions, finite difference, functional equations, approximations and expansions, and symbolic/algebraic manipulation.