03378nam 22006612 450 991045249510332120151005020623.01-139-88724-61-107-08985-91-107-10172-71-107-10416-50-511-75362-41-107-09613-81-107-09306-6(CKB)2550000001095237(EBL)1179122(OCoLC)850149014(SSID)ssj0000834732(PQKBManifestationID)11412027(PQKBTitleCode)TC0000834732(PQKBWorkID)10981603(PQKB)10585482(UkCbUP)CR9780511753626(MiAaPQ)EBC1179122(Au-PeEL)EBL1179122(CaPaEBR)ebr10718044(CaONFJC)MIL501984(EXLCZ)99255000000109523720100422d2011|||| uy| 0engur|||||||||||txtrdacontentcrdamediacrrdacarrierHadamard Expansions and Hyperasymptotic Evaluation an Extension of the Method of Steepest Descents /R.B. Paris[electronic resource]Cambridge :Cambridge University Press,2011.1 online resource (viii, 243 pages) digital, PDF file(s)Encyclopedia of mathematics and its applications ;volume 141Title from publisher's bibliographic system (viewed on 05 Oct 2015).1-107-00258-3 1-299-70733-5 Includes bibliographical references (p. 235-240) and index.Preface; 1. Asymptotics of Laplace-type integrals; 2. Hadamard expansion of Laplace integrals; 3. Hadamard expansion of Laplace-type integrals; 4. Applications.The author describes the recently developed theory of Hadamard expansions applied to the high-precision (hyperasymptotic) evaluation of Laplace and Laplace-type integrals. This brand new method builds on the well-known asymptotic method of steepest descents, of which the opening chapter gives a detailed account illustrated by a series of examples of increasing complexity. A discussion of uniformity problems associated with various coalescence phenomena, the Stokes phenomenon and hyperasymptotics of Laplace-type integrals follows. The remaining chapters deal with the Hadamard expansion of Laplace integrals, with and without saddle points. Problems of different types of saddle coalescence are also discussed. The text is illustrated with many numerical examples, which help the reader to understand the level of accuracy achievable. The author also considers applications to some important special functions. This book is ideal for graduate students and researchers working in asymptotics.Encyclopedia of mathematics and its applications ;v. 141.Hadamard Expansions & Hyperasymptotic EvaluationIntegral equationsAsymptotic theoryAsymptotic expansionsIntegral equationsAsymptotic theory.Asymptotic expansions.515/.45Paris R. B.441786UkCbUPUkCbUPBOOK9910452495103321Hadamard Expansions and Hyperasymptotic Evaluation1905635UNINA