Orthogonal polynomials and continued fractions: from Euler's point of view
Continued fractions, studied since Ancient Greece, only became a powerful tool in the eighteenth century, in the hands of the great mathematician Euler. This book tells how Euler introduced the idea of orthogonal polynomials and combined the two subjects, and how Brouncker's formula of 1655 can...
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2008
|
| Series: | Encyclopedia of mathematics and its applications
volume 122 |
| Subjects: | |
| Online Access: | BSB01 FHN01 URL des Erstveröffentlichers |
| Summary: | Continued fractions, studied since Ancient Greece, only became a powerful tool in the eighteenth century, in the hands of the great mathematician Euler. This book tells how Euler introduced the idea of orthogonal polynomials and combined the two subjects, and how Brouncker's formula of 1655 can be derived from Euler's efforts in Special Functions and Orthogonal Polynomials. The most interesting applications of this work are discussed, including the great Markoff's Theorem on the Lagrange spectrum, Abel's Theorem on integration in finite terms, Chebyshev's Theory of Orthogonal Polynomials, and very recent advances in Orthogonal Polynomials on the unit circle. As continued fractions become more important again, in part due to their use in finding algorithms in approximation theory, this timely book revives the approach of Wallis, Brouncker and Euler and illustrates the continuing significance of their influence. A translation of Euler's famous paper 'Continued Fractions, Observation' is included as an Addendum |
| Item Description: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Physical Description: | 1 online resource (xvi, 478 pages) |
| ISBN: | 9780511721403 |
| DOI: | 10.1017/CBO9780511721403 |
Staff View
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| 520 | |a Continued fractions, studied since Ancient Greece, only became a powerful tool in the eighteenth century, in the hands of the great mathematician Euler. This book tells how Euler introduced the idea of orthogonal polynomials and combined the two subjects, and how Brouncker's formula of 1655 can be derived from Euler's efforts in Special Functions and Orthogonal Polynomials. The most interesting applications of this work are discussed, including the great Markoff's Theorem on the Lagrange spectrum, Abel's Theorem on integration in finite terms, Chebyshev's Theory of Orthogonal Polynomials, and very recent advances in Orthogonal Polynomials on the unit circle. As continued fractions become more important again, in part due to their use in finding algorithms in approximation theory, this timely book revives the approach of Wallis, Brouncker and Euler and illustrates the continuing significance of their influence. A translation of Euler's famous paper 'Continued Fractions, Observation' is included as an Addendum | ||
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Record in the Search Index
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| any_adam_object | |
| author | Khrushchev, S. V. |
| author_facet | Khrushchev, S. V. |
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| bvnumber | BV043941769 |
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| collection | ZDB-20-CBO |
| contents | Continued fractions: real numbers -- Continued fractions: algebra -- Continued fractions: analysis -- Continued fractions: Euler -- Continued fractions: Euler's influence -- P-fractions -- Orthogonal polynomials -- Orthogonal polynomials on the unit circle -- Appendix. Continued fractions, observations L. Euler (1739) |
| ctrlnum | (ZDB-20-CBO)CR9780511721403 (OCoLC)850901343 (DE-599)BVBBV043941769 |
| dewey-full | 515.55 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.55 |
| dewey-search | 515.55 |
| dewey-sort | 3515.55 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511721403 |
| format | Electronic eBook |
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| id | DE-604.BV043941769 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:16Z |
| institution | BVB |
| isbn | 9780511721403 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029350739 |
| oclc_num | 850901343 |
| open_access_boolean | |
| owner | DE-12 DE-92 |
| owner_facet | DE-12 DE-92 |
| physical | 1 online resource (xvi, 478 pages) |
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| publishDate | 2008 |
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| publisher | Cambridge University Press |
| record_format | marc |
| series2 | Encyclopedia of mathematics and its applications |
| spelling | Khrushchev, S. V. Verfasser aut Orthogonal polynomials and continued fractions from Euler's point of view Sergey Khrushchev Orthogonal Polynomials & Continued Fractions Cambridge Cambridge University Press 2008 1 online resource (xvi, 478 pages) txt rdacontent c rdamedia cr rdacarrier Encyclopedia of mathematics and its applications volume 122 Title from publisher's bibliographic system (viewed on 05 Oct 2015) Continued fractions: real numbers -- Continued fractions: algebra -- Continued fractions: analysis -- Continued fractions: Euler -- Continued fractions: Euler's influence -- P-fractions -- Orthogonal polynomials -- Orthogonal polynomials on the unit circle -- Appendix. Continued fractions, observations L. Euler (1739) Continued fractions, studied since Ancient Greece, only became a powerful tool in the eighteenth century, in the hands of the great mathematician Euler. This book tells how Euler introduced the idea of orthogonal polynomials and combined the two subjects, and how Brouncker's formula of 1655 can be derived from Euler's efforts in Special Functions and Orthogonal Polynomials. The most interesting applications of this work are discussed, including the great Markoff's Theorem on the Lagrange spectrum, Abel's Theorem on integration in finite terms, Chebyshev's Theory of Orthogonal Polynomials, and very recent advances in Orthogonal Polynomials on the unit circle. As continued fractions become more important again, in part due to their use in finding algorithms in approximation theory, this timely book revives the approach of Wallis, Brouncker and Euler and illustrates the continuing significance of their influence. A translation of Euler's famous paper 'Continued Fractions, Observation' is included as an Addendum Euler, Leonhard / 1707-1783 Euler, Leonhard 1707-1783 (DE-588)118531379 gnd rswk-swf Orthogonal polynomials Continued fractions Kettenbruch (DE-588)4030401-2 gnd rswk-swf Orthogonale Polynome (DE-588)4172863-4 gnd rswk-swf Euler, Leonhard 1707-1783 (DE-588)118531379 p Orthogonale Polynome (DE-588)4172863-4 s Kettenbruch (DE-588)4030401-2 s 1\p DE-604 Erscheint auch als Druckausgabe 978-0-521-85419-1 https://doi.org/10.1017/CBO9780511721403 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Khrushchev, S. V. Orthogonal polynomials and continued fractions from Euler's point of view Continued fractions: real numbers -- Continued fractions: algebra -- Continued fractions: analysis -- Continued fractions: Euler -- Continued fractions: Euler's influence -- P-fractions -- Orthogonal polynomials -- Orthogonal polynomials on the unit circle -- Appendix. Continued fractions, observations L. Euler (1739) Euler, Leonhard / 1707-1783 Euler, Leonhard 1707-1783 (DE-588)118531379 gnd Orthogonal polynomials Continued fractions Kettenbruch (DE-588)4030401-2 gnd Orthogonale Polynome (DE-588)4172863-4 gnd |
| subject_GND | (DE-588)118531379 (DE-588)4030401-2 (DE-588)4172863-4 |
| title | Orthogonal polynomials and continued fractions from Euler's point of view |
| title_alt | Orthogonal Polynomials & Continued Fractions |
| title_auth | Orthogonal polynomials and continued fractions from Euler's point of view |
| title_exact_search | Orthogonal polynomials and continued fractions from Euler's point of view |
| title_full | Orthogonal polynomials and continued fractions from Euler's point of view Sergey Khrushchev |
| title_fullStr | Orthogonal polynomials and continued fractions from Euler's point of view Sergey Khrushchev |
| title_full_unstemmed | Orthogonal polynomials and continued fractions from Euler's point of view Sergey Khrushchev |
| title_short | Orthogonal polynomials and continued fractions |
| title_sort | orthogonal polynomials and continued fractions from euler s point of view |
| title_sub | from Euler's point of view |
| topic | Euler, Leonhard / 1707-1783 Euler, Leonhard 1707-1783 (DE-588)118531379 gnd Orthogonal polynomials Continued fractions Kettenbruch (DE-588)4030401-2 gnd Orthogonale Polynome (DE-588)4172863-4 gnd |
| topic_facet | Euler, Leonhard / 1707-1783 Euler, Leonhard 1707-1783 Orthogonal polynomials Continued fractions Kettenbruch Orthogonale Polynome |
| url | https://doi.org/10.1017/CBO9780511721403 |
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