Asymptotic expansions:
Certain functions, capable of expansion only as a divergent series, may nevertheless be calculated with great accuracy by taking the sum of a suitable number of terms. The theory of such asymptotic expansions is of great importance in many branches of pure and applied mathematics and in theoretical...
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
1965
|
| Series: | Cambridge tracts in mathematics
55 |
| Subjects: | |
| Online Access: | BSB01 FHN01 UBR01 Volltext |
| Summary: | Certain functions, capable of expansion only as a divergent series, may nevertheless be calculated with great accuracy by taking the sum of a suitable number of terms. The theory of such asymptotic expansions is of great importance in many branches of pure and applied mathematics and in theoretical physics. Solutions of ordinary differential equations are frequently obtained in the form of a definite integral or contour integral, and this tract is concerned with the asymptotic representation of a function of a real or complex variable defined in this way. After a preliminary account of the properties of asymptotic series, the standard methods of deriving the asymptotic expansion of an integral are explained in detail and illustrated by the expansions of various special functions. These methods include integration by parts, Laplace's approximation, Watson's lemma on Laplace transforms, the method of steepest descents, and the saddle-point method. The last two chapters deal with Airy's integral and uniform asymptotic expansions |
| Physical Description: | 1 Online-Ressource (viii, 120 Seiten) |
| ISBN: | 9780511526121 |
| DOI: | 10.1017/CBO9780511526121 |
Staff View
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| 490 | 0 | |a Cambridge tracts in mathematics |v 55 | |
| 505 | 8 | |a Introduction -- Preliminaries -- Integration by parts -- The method of stationary phase -- The method of Laplace -- Watson's lemma -- The method of steepest descents -- The saddle-point method -- Airy's integral -- Uniform asymptotic expansions | |
| 520 | |a Certain functions, capable of expansion only as a divergent series, may nevertheless be calculated with great accuracy by taking the sum of a suitable number of terms. The theory of such asymptotic expansions is of great importance in many branches of pure and applied mathematics and in theoretical physics. Solutions of ordinary differential equations are frequently obtained in the form of a definite integral or contour integral, and this tract is concerned with the asymptotic representation of a function of a real or complex variable defined in this way. After a preliminary account of the properties of asymptotic series, the standard methods of deriving the asymptotic expansion of an integral are explained in detail and illustrated by the expansions of various special functions. These methods include integration by parts, Laplace's approximation, Watson's lemma on Laplace transforms, the method of steepest descents, and the saddle-point method. The last two chapters deal with Airy's integral and uniform asymptotic expansions | ||
| 650 | 4 | |a Asymptotic expansions | |
| 650 | 4 | |a Integrals | |
| 650 | 0 | 7 | |a Asymptotische Entwicklung |0 (DE-588)4112609-9 |2 gnd |9 rswk-swf |
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Record in the Search Index
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| any_adam_object | |
| author | Copson, Edward T. 1901-1980 |
| author_GND | (DE-588)174094388 |
| author_facet | Copson, Edward T. 1901-1980 |
| author_role | aut |
| author_sort | Copson, Edward T. 1901-1980 |
| author_variant | e t c et etc |
| building | Verbundindex |
| bvnumber | BV043942315 |
| classification_rvk | SK 750 |
| collection | ZDB-20-CBO |
| contents | Introduction -- Preliminaries -- Integration by parts -- The method of stationary phase -- The method of Laplace -- Watson's lemma -- The method of steepest descents -- The saddle-point method -- Airy's integral -- Uniform asymptotic expansions |
| ctrlnum | (ZDB-20-CBO)CR9780511526121 (OCoLC)732170600 (DE-599)BVBBV043942315 |
| dewey-full | 515.35 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.35 |
| dewey-search | 515.35 |
| dewey-sort | 3515.35 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511526121 |
| format | Electronic eBook |
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| id | DE-604.BV043942315 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:17Z |
| institution | BVB |
| isbn | 9780511526121 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029351285 |
| oclc_num | 732170600 |
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| owner_facet | DE-12 DE-92 DE-355 DE-BY-UBR |
| physical | 1 Online-Ressource (viii, 120 Seiten) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO ZDB-20-CBO UBR Einzelkauf (Lückenergänzung CUP Serien 2018) |
| publishDate | 1965 |
| publishDateSearch | 1965 |
| publishDateSort | 1965 |
| publisher | Cambridge University Press |
| record_format | marc |
| series2 | Cambridge tracts in mathematics |
| spelling | Copson, Edward T. 1901-1980 Verfasser (DE-588)174094388 aut Asymptotic expansions by E.T. Copson Cambridge Cambridge University Press 1965 1 Online-Ressource (viii, 120 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge tracts in mathematics 55 Introduction -- Preliminaries -- Integration by parts -- The method of stationary phase -- The method of Laplace -- Watson's lemma -- The method of steepest descents -- The saddle-point method -- Airy's integral -- Uniform asymptotic expansions Certain functions, capable of expansion only as a divergent series, may nevertheless be calculated with great accuracy by taking the sum of a suitable number of terms. The theory of such asymptotic expansions is of great importance in many branches of pure and applied mathematics and in theoretical physics. Solutions of ordinary differential equations are frequently obtained in the form of a definite integral or contour integral, and this tract is concerned with the asymptotic representation of a function of a real or complex variable defined in this way. After a preliminary account of the properties of asymptotic series, the standard methods of deriving the asymptotic expansion of an integral are explained in detail and illustrated by the expansions of various special functions. These methods include integration by parts, Laplace's approximation, Watson's lemma on Laplace transforms, the method of steepest descents, and the saddle-point method. The last two chapters deal with Airy's integral and uniform asymptotic expansions Asymptotic expansions Integrals Asymptotische Entwicklung (DE-588)4112609-9 gnd rswk-swf Asymptotische Entwicklung (DE-588)4112609-9 s DE-604 Erscheint auch als Druck-Ausgabe 978-0-521-04721-0 Erscheint auch als Druck-Ausgabe 978-0-521-60482-6 https://doi.org/10.1017/CBO9780511526121 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Copson, Edward T. 1901-1980 Asymptotic expansions Introduction -- Preliminaries -- Integration by parts -- The method of stationary phase -- The method of Laplace -- Watson's lemma -- The method of steepest descents -- The saddle-point method -- Airy's integral -- Uniform asymptotic expansions Asymptotic expansions Integrals Asymptotische Entwicklung (DE-588)4112609-9 gnd |
| subject_GND | (DE-588)4112609-9 |
| title | Asymptotic expansions |
| title_auth | Asymptotic expansions |
| title_exact_search | Asymptotic expansions |
| title_full | Asymptotic expansions by E.T. Copson |
| title_fullStr | Asymptotic expansions by E.T. Copson |
| title_full_unstemmed | Asymptotic expansions by E.T. Copson |
| title_short | Asymptotic expansions |
| title_sort | asymptotic expansions |
| topic | Asymptotic expansions Integrals Asymptotische Entwicklung (DE-588)4112609-9 gnd |
| topic_facet | Asymptotic expansions Integrals Asymptotische Entwicklung |
| url | https://doi.org/10.1017/CBO9780511526121 |
| work_keys_str_mv | AT copsonedwardt asymptoticexpansions |