The Stokes phenomenon, Borel summation and Mellin-Barnes regularisation /
Kowalenko, Victor, 1956-
The Stokes phenomenon, Borel summation and Mellin-Barnes regularisation / Victor Kowalenko. - 1 online resource (xi, 249 pages)
Includes bibliographical references (pages 239-243) and indexes.
The Stokes Phenomenon, Borel Summation; 9781608050109.jpg.pdf; Cover Page; Contents; Chapter-1; Chapter-2; Chapter-3; Chapter-4; Chapter-5; Chapter-6; Chapter-7; Chapter-8; Chapter-9; Chapter-10; Chapter-11; Chapter-12; Appendix; References; Author Index; Subject Index
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.
9781608050109 (electronic book) 1608050106 (electronic book)
Integrals.
Intégrales.
MATHEMATICS--Differential Equations--General.
Integrals.
Electronic books.
QA308 / .K69 2009
515/.354
The Stokes phenomenon, Borel summation and Mellin-Barnes regularisation / Victor Kowalenko. - 1 online resource (xi, 249 pages)
Includes bibliographical references (pages 239-243) and indexes.
The Stokes Phenomenon, Borel Summation; 9781608050109.jpg.pdf; Cover Page; Contents; Chapter-1; Chapter-2; Chapter-3; Chapter-4; Chapter-5; Chapter-6; Chapter-7; Chapter-8; Chapter-9; Chapter-10; Chapter-11; Chapter-12; Appendix; References; Author Index; Subject Index
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.
9781608050109 (electronic book) 1608050106 (electronic book)
Integrals.
Intégrales.
MATHEMATICS--Differential Equations--General.
Integrals.
Electronic books.
QA308 / .K69 2009
515/.354