The Stokes Phenomenon, Borel Summation and Mellin-Barnes Regularisation

Download or read book The Stokes Phenomenon, Borel Summation and Mellin-Barnes Regularisation written by Victor Kowalenko and published by Bentham Science Publishers. This book was released on 2009 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 disc