Asymptotics and Mellin-Barnes Integrals


Asymptotics and Mellin-Barnes Integrals provides an account of the use and properties of a type of complex integral representation that arises frequently in the study of special functions typically of interest in classical analysis and mathematical physics. After developing the properties of these integrals, their use in determining the asymptotic behavior of special functions is detailed. Although such integrals have a long history, the book's account includes recent research results in analytic number theory and hyperasymptotics. The book also fills a gap in the literature on asymptotic analysis and special functions by providing a thorough account of the use of Mellin-Barnes integrals that is otherwise not available in standard references on asymptotics.


 Reviews:

"This book is very valuable for the asymptotic community....It is the first book to contain a detailed introduction to hyperasymptotics." SIAM Review

"This book is a very welcome addition... I can highly recommend this book to anyone interested in asymptotics of integrals or in asymptotic methods for special functions." Mathematics of Computation