Asymptotics and Mellin-Barnes Integrals

Provides an account of the use and properties of a type of complex integral representation that arises in the study of special functions.

R. B. Paris (Author), D. Kaminski (Author)

9780521790017, Cambridge University Press

Hardback, published 24 September 2001

440 pages, 71 b/w illus.
24.3 x 16.3 x 2.8 cm, 0.773 kg

'Asymptotics and Mellin-Barnes integrals by R. B. Paris and D. Kaminski is one of the first new, extended texts to be published in English since the recent advances began, and is a mixture of existing and novel techniques and applications. … but the comprehensive nature of this work means that it is likely to become one of the most significant textbook references for Mellin-Barnes theory. Every university with physical scientists, engineers or mathematicians who use asymptotic expansions should have at least one copy of this book.' Bulletin of the London Mathematical Society

Asymptotics and Mellin-Barnes Integrals, first published in 2001, 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 behaviour 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 other standard references on asymptotics.

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.

Subject Areas: Applied mathematics [PBW], Calculus & mathematical analysis [PBK]