Generalised Euler-Jacobi inversion formula and asymptotics beyond all orders:
This work, first published in 1995, presents developments in understanding the subdominant exponential terms of asymptotic expansions which have previously been neglected. By considering special exponential series arising in number theory, the authors derive the generalised Euler-Jacobi series, expr...
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
1995
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| Series: | London Mathematical Society lecture note series
214 |
| Subjects: | |
| Online Access: | BSB01 FHN01 Volltext |
| Summary: | This work, first published in 1995, presents developments in understanding the subdominant exponential terms of asymptotic expansions which have previously been neglected. By considering special exponential series arising in number theory, the authors derive the generalised Euler-Jacobi series, expressed in terms of hypergeometric series. Dingle's theory of terminants is then employed to show how the divergences in both dominant and subdominant series of a complete asymptotic expansion can be tamed. Numerical results are used to illustrate that a complete asymptotic expansion can be made to agree with exact results for the generalised Euler-Jacobi series to any desired degree of accuracy. All researchers interested in the fascinating area of exponential asymptotics will find this a most valuable book |
| Item Description: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Physical Description: | 1 online resource (x, 129 pages) |
| ISBN: | 9780511752513 |
| DOI: | 10.1017/CBO9780511752513 |
Staff View
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| 245 | 1 | 0 | |a Generalised Euler-Jacobi inversion formula and asymptotics beyond all orders |c V. Kowalenko [and others] |
| 246 | 1 | 3 | |a Generalised Euler-Jacobi Inversion Formula & Asymptotics beyond All Orders |
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| 500 | |a Title from publisher's bibliographic system (viewed on 05 Oct 2015) | ||
| 505 | 8 | |a Introduction -- Exact evaluation of S[superscript r subscript p/q] (a) -- Properties of S[subscript p/q] (a) -- Steepest descent -- Special cases of S[subscript p/q] (a) for p/q <2 -- Integer cases for S[subscript p/q] (a) where 2 <̲ p/q <̲ 7 -- Asymptotics beyond all orders -- Numerics for terminant sums -- Conclusion | |
| 520 | |a This work, first published in 1995, presents developments in understanding the subdominant exponential terms of asymptotic expansions which have previously been neglected. By considering special exponential series arising in number theory, the authors derive the generalised Euler-Jacobi series, expressed in terms of hypergeometric series. Dingle's theory of terminants is then employed to show how the divergences in both dominant and subdominant series of a complete asymptotic expansion can be tamed. Numerical results are used to illustrate that a complete asymptotic expansion can be made to agree with exact results for the generalised Euler-Jacobi series to any desired degree of accuracy. All researchers interested in the fascinating area of exponential asymptotics will find this a most valuable book | ||
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Record in the Search Index
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| any_adam_object | |
| author | Kowalenko, V. |
| author_facet | Kowalenko, V. |
| author_role | aut |
| author_sort | Kowalenko, V. |
| author_variant | v k vk |
| building | Verbundindex |
| bvnumber | BV043941264 |
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| collection | ZDB-20-CBO |
| contents | Introduction -- Exact evaluation of S[superscript r subscript p/q] (a) -- Properties of S[subscript p/q] (a) -- Steepest descent -- Special cases of S[subscript p/q] (a) for p/q <2 -- Integer cases for S[subscript p/q] (a) where 2 <̲ p/q <̲ 7 -- Asymptotics beyond all orders -- Numerics for terminant sums -- Conclusion |
| ctrlnum | (ZDB-20-CBO)CR9780511752513 (OCoLC)967600479 (DE-599)BVBBV043941264 |
| dewey-full | 515/.234 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.234 |
| dewey-search | 515/.234 |
| dewey-sort | 3515 3234 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511752513 |
| format | Electronic eBook |
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| id | DE-604.BV043941264 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:15Z |
| institution | BVB |
| isbn | 9780511752513 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029350235 |
| oclc_num | 967600479 |
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| owner_facet | DE-12 DE-92 |
| physical | 1 online resource (x, 129 pages) |
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| publishDate | 1995 |
| publishDateSearch | 1995 |
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| publisher | Cambridge University Press |
| record_format | marc |
| series2 | London Mathematical Society lecture note series |
| spelling | Kowalenko, V. Verfasser aut Generalised Euler-Jacobi inversion formula and asymptotics beyond all orders V. Kowalenko [and others] Generalised Euler-Jacobi Inversion Formula & Asymptotics beyond All Orders Cambridge Cambridge University Press 1995 1 online resource (x, 129 pages) txt rdacontent c rdamedia cr rdacarrier London Mathematical Society lecture note series 214 Title from publisher's bibliographic system (viewed on 05 Oct 2015) Introduction -- Exact evaluation of S[superscript r subscript p/q] (a) -- Properties of S[subscript p/q] (a) -- Steepest descent -- Special cases of S[subscript p/q] (a) for p/q <2 -- Integer cases for S[subscript p/q] (a) where 2 <̲ p/q <̲ 7 -- Asymptotics beyond all orders -- Numerics for terminant sums -- Conclusion This work, first published in 1995, presents developments in understanding the subdominant exponential terms of asymptotic expansions which have previously been neglected. By considering special exponential series arising in number theory, the authors derive the generalised Euler-Jacobi series, expressed in terms of hypergeometric series. Dingle's theory of terminants is then employed to show how the divergences in both dominant and subdominant series of a complete asymptotic expansion can be tamed. Numerical results are used to illustrate that a complete asymptotic expansion can be made to agree with exact results for the generalised Euler-Jacobi series to any desired degree of accuracy. All researchers interested in the fascinating area of exponential asymptotics will find this a most valuable book Jacobi series Asymptotic expansions Thetafunktion (DE-588)4185175-4 gnd rswk-swf Euler-Jacobi-Reihe (DE-588)4413705-9 gnd rswk-swf Euler-Jacobi-Reihe (DE-588)4413705-9 s 1\p DE-604 Thetafunktion (DE-588)4185175-4 s 2\p DE-604 Erscheint auch als Druckausgabe 978-0-521-49798-5 https://doi.org/10.1017/CBO9780511752513 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Kowalenko, V. Generalised Euler-Jacobi inversion formula and asymptotics beyond all orders Introduction -- Exact evaluation of S[superscript r subscript p/q] (a) -- Properties of S[subscript p/q] (a) -- Steepest descent -- Special cases of S[subscript p/q] (a) for p/q <2 -- Integer cases for S[subscript p/q] (a) where 2 <̲ p/q <̲ 7 -- Asymptotics beyond all orders -- Numerics for terminant sums -- Conclusion Jacobi series Asymptotic expansions Thetafunktion (DE-588)4185175-4 gnd Euler-Jacobi-Reihe (DE-588)4413705-9 gnd |
| subject_GND | (DE-588)4185175-4 (DE-588)4413705-9 |
| title | Generalised Euler-Jacobi inversion formula and asymptotics beyond all orders |
| title_alt | Generalised Euler-Jacobi Inversion Formula & Asymptotics beyond All Orders |
| title_auth | Generalised Euler-Jacobi inversion formula and asymptotics beyond all orders |
| title_exact_search | Generalised Euler-Jacobi inversion formula and asymptotics beyond all orders |
| title_full | Generalised Euler-Jacobi inversion formula and asymptotics beyond all orders V. Kowalenko [and others] |
| title_fullStr | Generalised Euler-Jacobi inversion formula and asymptotics beyond all orders V. Kowalenko [and others] |
| title_full_unstemmed | Generalised Euler-Jacobi inversion formula and asymptotics beyond all orders V. Kowalenko [and others] |
| title_short | Generalised Euler-Jacobi inversion formula and asymptotics beyond all orders |
| title_sort | generalised euler jacobi inversion formula and asymptotics beyond all orders |
| topic | Jacobi series Asymptotic expansions Thetafunktion (DE-588)4185175-4 gnd Euler-Jacobi-Reihe (DE-588)4413705-9 gnd |
| topic_facet | Jacobi series Asymptotic expansions Thetafunktion Euler-Jacobi-Reihe |
| url | https://doi.org/10.1017/CBO9780511752513 |
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