Asymptotics and Mellin-Barnes integrals
著者
書誌事項
Asymptotics and Mellin-Barnes integrals
（Encyclopedia of mathematics and its applications / edited by G.-C. Rota, v. 85）
Cambridge University Press, 2001
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注記
Bibliography: p. [409]-418
Includes index
内容説明・目次
内容説明
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.
目次
- 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.
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