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200 10$aHadamard Expansions and Hyperasymptotic Evaluation $ean Extension of the Method of Steepest Descents /$fR.B. Paris$b[electronic resource]
210  1$aCambridge :$cCambridge University Press,$d2011.
215   $a1 online resource (viii, 243 pages) $cdigital, PDF file(s)
225 1 $aEncyclopedia of mathematics and its applications ;$vvolume 141
300   $aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
311   $a1-107-00258-3 
311   $a1-299-70733-5 
320   $aIncludes bibliographical references (p. 235-240) and index.
327   $aPreface; 1. Asymptotics of Laplace-type integrals; 2. Hadamard expansion of Laplace integrals; 3. Hadamard expansion of Laplace-type integrals; 4. Applications.
330   $aThe author describes the recently developed theory of Hadamard expansions applied to the high-precision (hyperasymptotic) evaluation of Laplace and Laplace-type integrals. This brand new method builds on the well-known asymptotic method of steepest descents, of which the opening chapter gives a detailed account illustrated by a series of examples of increasing complexity. A discussion of uniformity problems associated with various coalescence phenomena, the Stokes phenomenon and hyperasymptotics of Laplace-type integrals follows. The remaining chapters deal with the Hadamard expansion of Laplace integrals, with and without saddle points. Problems of different types of saddle coalescence are also discussed. The text is illustrated with many numerical examples, which help the reader to understand the level of accuracy achievable. The author also considers applications to some important special functions. This book is ideal for graduate students and researchers working in asymptotics.
410  0$aEncyclopedia of mathematics and its applications ;$vv. 141.
517 3 $aHadamard Expansions & Hyperasymptotic Evaluation
606   $aIntegral equations$xAsymptotic theory
606   $aAsymptotic expansions
615  0$aIntegral equations$xAsymptotic theory.
615  0$aAsymptotic expansions.
676   $a515/.45
686   $aMAT002010$2bisacsh
700   $aParis$b R. B.$0441786
801  0$bUkCbUP
801  1$bUkCbUP
906   $aBOOK
912   $a9910821896903321
996   $aHadamard Expansions and Hyperasymptotic Evaluation$93928996
997   $aUNINA