Hadamard expansions and hyperasymptotic evaluation: an extension of the method of steepest descents
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2011
|
| Schriftenreihe: | Encyclopedia of mathematics and its applications
141 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | VIII, 243 S. graph Darst. 24 cm |
| ISBN: | 9781107002586 1107002583 |
Internformat
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Datensatz im Suchindex
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| adam_text | Contents
Preface
page vii
Asymptotics of Laplace-type integrals
1
1
5
20
37
56
73
78
83
100
100
101
122
126
134
140
144
144
145
151
175
178
197
197
198
207
1.1
Historical introduction
1.2
The method of steepest descents
1.3
Examples
1.4
Further examples
1.5
Uniform expansions
1.6
Optimal truncation and superasymptotics
1.7
The Stokes phenomenon
1.8
Hyperasymptotics
Hadamard
expansion of Laplace integrals
2.1
Introduction
2.2
The
Hadamard
series for Iv(x)
2.3
Rapidly convergent
Hadamard
series
2.4
Hadamard
series on an infinite interval
2.5
Examples
2.6
Bounds on the tails of
Hadamard
series
Hadamard
expansion of Laplace-type integrals
3.1
Introduction
3.2
Expansion schemes
3.3
Examples
3.4
Coalescence problems
3.5
Examples of coalescence
Applications
4.1
Introduction
4.2
The Bessel function Jv(vz)
4.3
The Pearcey integral
VI
Contents
4.4
The parabolic cylinder function
4.5
The expansion for log
Γ (ζ)
Appendix A:
Appendix B:
Appendix C:
References
Index
Properties of
Ρ
(a, z)
Convergence of
Hadamard
series
Connection with the exp-arc integrals
216
219
224
230
232
235
241
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 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.
R
.
в
.
paris
is a Reader in Mathematics at the University of Abertay, Dundee.
Encyclopedia of Mathematics and Its Applications
This series is devoted to significant topics or themes that have wide application in
mathematics or mathematical science and for which a detailed development of the
abstract theory is less important than a thorough and concrete exploration of the
implications and applications.
Books in the Encyclopedia of Mathematics and Its Applications cover their
subjects comprehensively. Less important results may be summarized as exercises
at the ends of chapters. For technicalities, readers can be referred to the
bibliography, which is expected to be comprehensive. As a result, volumes are
encyclopedic references or manageable guides to major subjects.
|
| any_adam_object | 1 |
| author | Paris, Richard B. 1946- |
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| author_facet | Paris, Richard B. 1946- |
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| author_sort | Paris, Richard B. 1946- |
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| building | Verbundindex |
| bvnumber | BV037344220 |
| classification_rvk | SK 450 |
| classification_tum | MAT 440f MAT 418f |
| ctrlnum | (OCoLC)712387424 (DE-599)BSZ338369376 |
| dewey-full | 515.723 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.723 |
| dewey-search | 515.723 |
| dewey-sort | 3515.723 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV037344220 |
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| isbn | 9781107002586 1107002583 |
| language | English |
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| series | Encyclopedia of mathematics and its applications |
| series2 | Encyclopedia of mathematics and its applications |
| spelling | Paris, Richard B. 1946- Verfasser (DE-588)143980289 aut Hadamard expansions and hyperasymptotic evaluation an extension of the method of steepest descents R. B. Paris Cambridge [u.a.] Cambridge Univ. Press 2011 VIII, 243 S. graph Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Encyclopedia of mathematics and its applications 141 Integralgleichung (DE-588)4027229-1 gnd rswk-swf Asymptotische Entwicklung (DE-588)4112609-9 gnd rswk-swf Laplace-Transformation (DE-588)4034577-4 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Asymptotik (DE-588)4126634-1 gnd rswk-swf Integral equations / Asymptotic theory Laplace transformation Integralgleichung (DE-588)4027229-1 s Asymptotik (DE-588)4126634-1 s DE-604 Laplace-Transformation (DE-588)4034577-4 s Asymptotische Entwicklung (DE-588)4112609-9 s Numerisches Verfahren (DE-588)4128130-5 s Encyclopedia of mathematics and its applications 141 (DE-604)BV000903719 141 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022497865&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022497865&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext 1. publ. |
| spellingShingle | Paris, Richard B. 1946- Hadamard expansions and hyperasymptotic evaluation an extension of the method of steepest descents Encyclopedia of mathematics and its applications Integralgleichung (DE-588)4027229-1 gnd Asymptotische Entwicklung (DE-588)4112609-9 gnd Laplace-Transformation (DE-588)4034577-4 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Asymptotik (DE-588)4126634-1 gnd |
| subject_GND | (DE-588)4027229-1 (DE-588)4112609-9 (DE-588)4034577-4 (DE-588)4128130-5 (DE-588)4126634-1 |
| 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 | Integralgleichung (DE-588)4027229-1 gnd Asymptotische Entwicklung (DE-588)4112609-9 gnd Laplace-Transformation (DE-588)4034577-4 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Asymptotik (DE-588)4126634-1 gnd |
| topic_facet | Integralgleichung Asymptotische Entwicklung Laplace-Transformation Numerisches Verfahren Asymptotik |
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