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.

• Spans the history of the subject: from fundamental properties of Mellin-Barnes integrals and Mellin transforms to recent research results
• The mathematics developed is completely rigorous and well-illustrated by numerical examples
• The text is accessible to anyone with a grounding in undergraduate complex analysis, and so can prove to be of value to non-mathematicians
• Numerous historical references appear throughout the book, which contains a comprehensive bibliography of over two hundred items