The Stokes phenomenon refers to the emergence of jump discontinuities
in asymptotic expansions at specific rays in the complex plane.
This book presents a radical theory for the phenomenon by introducing
the concept of regularization. Two methods of regularization, Borel
summation and Mellin-Barnes regularization, are used to derive general
expressions for the regularized values of asymptotic expansions
throughout the complex plane. Though different, both yield identical
values, which, where possible, agree with the original functions.
Consequently, asymptotics has been elevated to a true discipline
yielding precise solutions. All researchers, who seek asymptotic
solutions to problems, will find this a most valuable book.