Hadamard expansions and hyperasymptotic evaluation: an extension of the method of steepest descents
"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...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge ; New York
Cambridge University Press
2011
|
| Schriftenreihe: | Encyclopedia of mathematics and its applications
141 |
| Schlagworte: | |
| Zusammenfassung: | "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"-- |
| Beschreibung: | viii, 243 p. ill |
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| 100 | 1 | |a Paris, R. B. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Hadamard expansions and hyperasymptotic evaluation |b an extension of the method of steepest descents |c R.B. Paris |
| 264 | 1 | |a Cambridge ; New York |b Cambridge University Press |c 2011 | |
| 300 | |a viii, 243 p. |b ill | ||
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| 490 | 0 | |a Encyclopedia of mathematics and its applications |v 141 | |
| 520 | |a "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"-- | ||
| 650 | 4 | |a Integral equations |x Asymptotic theory | |
| 650 | 4 | |a Asymptotic expansions | |
| 710 | 2 | |a ProQuest (Firm) |e Sonstige |4 oth | |
| 912 | |a ZDB-30-PAD | ||
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Datensatz im Suchindex
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|---|---|
| any_adam_object | |
| author | Paris, R. B. |
| author_facet | Paris, R. B. |
| author_role | aut |
| author_sort | Paris, R. B. |
| author_variant | r b p rb rbp |
| building | Verbundindex |
| bvnumber | BV045253597 |
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| dewey-full | 515/.45 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.45 |
| dewey-search | 515/.45 |
| dewey-sort | 3515 245 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV045253597 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T08:12:54Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030641573 |
| oclc_num | 850149014 |
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| physical | viii, 243 p. ill |
| psigel | ZDB-30-PAD |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Cambridge University Press |
| record_format | marc |
| series2 | Encyclopedia of mathematics and its applications |
| spelling | Paris, R. B. Verfasser aut Hadamard expansions and hyperasymptotic evaluation an extension of the method of steepest descents R.B. Paris Cambridge ; New York Cambridge University Press 2011 viii, 243 p. ill txt rdacontent c rdamedia cr rdacarrier Encyclopedia of mathematics and its applications 141 "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"-- Integral equations Asymptotic theory Asymptotic expansions ProQuest (Firm) Sonstige oth |
| spellingShingle | Paris, R. B. Hadamard expansions and hyperasymptotic evaluation an extension of the method of steepest descents Integral equations Asymptotic theory Asymptotic expansions |
| title | Hadamard expansions and hyperasymptotic evaluation an extension of the method of steepest descents |
| title_auth | Hadamard expansions and hyperasymptotic evaluation an extension of the method of steepest descents |
| title_exact_search | Hadamard expansions and hyperasymptotic evaluation an extension of the method of steepest descents |
| title_full | Hadamard expansions and hyperasymptotic evaluation an extension of the method of steepest descents R.B. Paris |
| title_fullStr | Hadamard expansions and hyperasymptotic evaluation an extension of the method of steepest descents R.B. Paris |
| title_full_unstemmed | Hadamard expansions and hyperasymptotic evaluation an extension of the method of steepest descents R.B. Paris |
| title_short | Hadamard expansions and hyperasymptotic evaluation |
| title_sort | hadamard expansions and hyperasymptotic evaluation an extension of the method of steepest descents |
| title_sub | an extension of the method of steepest descents |
| topic | Integral equations Asymptotic theory Asymptotic expansions |
| topic_facet | Integral equations Asymptotic theory Asymptotic expansions |
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