Asymptotics and Mellin-Barnes Integrals

by R. B. Paris, D. Kaminski

Overview

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.

Product Details

ISBN-13:	9780521790017
Publisher:	Cambridge University Press
Publication date:	09/24/2001
Series:	Encyclopedia of Mathematics and its Applications , #85
Pages:	440
Product dimensions:	6.30(w) x 9.40(h) x 1.10(d)

Table of Contents

1. Introduction; 2. Fundamental results; 3. Properties of Mellin transforms; 4. Applications of Mellin transforms; 5. Asymptotic expansions; 6. The Stokes phenomenon and hyperasymptotics; 7. Multiple Mellin-Barnes integrals; 8. Application to some special functions.

Editorial 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

From the Publisher

Paris (mathematics, U. of Abertay Dundee, UK) and Kaminski (U. of Lethbridge, Canada) explain the properties of Mellin-Barnes integrals and their applications to problems involving special functions, especially the determination of asymptotic expansions. The basic analytical properties of the integrals are examined for number theory, differential, and difference equations. Among the functions under examination are hypergeometric, Bessel, and parabolic cylinder functions. The Stokes phenomenon and hyperasymptotics are discussed. Finally the application of ideas presented earlier to higher- dimensional Laplace-type integrals, the Euler-Jacobi series, the Riemann zeta function, and the Pearcey integral are detailed. Annotation c. Book News, Inc., Portland, OR (booknews.com)