History of Continued Fractions and Padé Approximants:
Gespeichert in:
1. Verfasser: | |
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Format: | Elektronisch E-Book |
Sprache: | English |
Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1991
|
Schriftenreihe: | Springer Series in Computational Mathematics
12 |
Schlagworte: | |
Online-Zugang: | Volltext |
Beschreibung: | The history of continued fractions is certainly one of the longest among those of mathematical concepts, since it begins with Euclid's algorithm for the great est common divisor at least three centuries B.C. As it is often the case and like Monsieur Jourdain in Moliere's "Ie bourgeois gentilhomme" (who was speak ing in prose though he did not know he was doing so), continued fractions were used for many centuries before their real discovery. The history of continued fractions and Pade approximants is also quite im portant, since they played a leading role in the development of some branches of mathematics. For example, they were the basis for the proof of the tran scendence of 11' in 1882, an open problem for more than two thousand years, and also for our modern spectral theory of operators. Actually they still are of great interest in many fields of pure and applied mathematics and in numerical analysis, where they provide computer approximations to special functions and are connected to some convergence acceleration methods. Con tinued fractions are also used in number theory, computer science, automata, electronics, etc .. |
Beschreibung: | 1 Online-Ressource (VIII, 551 p) |
ISBN: | 9783642581694 9783642634888 |
ISSN: | 0179-3632 |
DOI: | 10.1007/978-3-642-58169-4 |
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author | Brezinski, Claude |
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dewey-tens | 510 - Mathematics |
discipline | Mathematik |
doi_str_mv | 10.1007/978-3-642-58169-4 |
era | Geschichte Anfänge-1939 gnd |
era_facet | Geschichte Anfänge-1939 |
format | Electronic eBook |
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spelling | Brezinski, Claude Verfasser aut History of Continued Fractions and Padé Approximants by Claude Brezinski Berlin, Heidelberg Springer Berlin Heidelberg 1991 1 Online-Ressource (VIII, 551 p) txt rdacontent c rdamedia cr rdacarrier Springer Series in Computational Mathematics 12 0179-3632 The history of continued fractions is certainly one of the longest among those of mathematical concepts, since it begins with Euclid's algorithm for the great est common divisor at least three centuries B.C. As it is often the case and like Monsieur Jourdain in Moliere's "Ie bourgeois gentilhomme" (who was speak ing in prose though he did not know he was doing so), continued fractions were used for many centuries before their real discovery. The history of continued fractions and Pade approximants is also quite im portant, since they played a leading role in the development of some branches of mathematics. For example, they were the basis for the proof of the tran scendence of 11' in 1882, an open problem for more than two thousand years, and also for our modern spectral theory of operators. Actually they still are of great interest in many fields of pure and applied mathematics and in numerical analysis, where they provide computer approximations to special functions and are connected to some convergence acceleration methods. Con tinued fractions are also used in number theory, computer science, automata, electronics, etc .. Geschichte Anfänge-1939 gnd rswk-swf Mathematics Global analysis (Mathematics) Numerical analysis Number theory Numerical Analysis Number Theory Analysis Mathematik Kettenbruch (DE-588)4030401-2 gnd rswk-swf Geschichte (DE-588)4020517-4 gnd rswk-swf Padé-Näherungsbruch (DE-588)4173061-6 gnd rswk-swf Bibliografie (DE-588)4006432-3 gnd rswk-swf Kettenbruch (DE-588)4030401-2 s Geschichte (DE-588)4020517-4 s 1\p DE-604 Padé-Näherungsbruch (DE-588)4173061-6 s 2\p DE-604 Bibliografie (DE-588)4006432-3 s 3\p DE-604 Geschichte Anfänge-1939 z 4\p DE-604 5\p DE-604 6\p DE-604 https://doi.org/10.1007/978-3-642-58169-4 Verlag 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 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 5\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 6\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
spellingShingle | Brezinski, Claude History of Continued Fractions and Padé Approximants Mathematics Global analysis (Mathematics) Numerical analysis Number theory Numerical Analysis Number Theory Analysis Mathematik Kettenbruch (DE-588)4030401-2 gnd Geschichte (DE-588)4020517-4 gnd Padé-Näherungsbruch (DE-588)4173061-6 gnd Bibliografie (DE-588)4006432-3 gnd |
subject_GND | (DE-588)4030401-2 (DE-588)4020517-4 (DE-588)4173061-6 (DE-588)4006432-3 |
title | History of Continued Fractions and Padé Approximants |
title_auth | History of Continued Fractions and Padé Approximants |
title_exact_search | History of Continued Fractions and Padé Approximants |
title_full | History of Continued Fractions and Padé Approximants by Claude Brezinski |
title_fullStr | History of Continued Fractions and Padé Approximants by Claude Brezinski |
title_full_unstemmed | History of Continued Fractions and Padé Approximants by Claude Brezinski |
title_short | History of Continued Fractions and Padé Approximants |
title_sort | history of continued fractions and pade approximants |
topic | Mathematics Global analysis (Mathematics) Numerical analysis Number theory Numerical Analysis Number Theory Analysis Mathematik Kettenbruch (DE-588)4030401-2 gnd Geschichte (DE-588)4020517-4 gnd Padé-Näherungsbruch (DE-588)4173061-6 gnd Bibliografie (DE-588)4006432-3 gnd |
topic_facet | Mathematics Global analysis (Mathematics) Numerical analysis Number theory Numerical Analysis Number Theory Analysis Mathematik Kettenbruch Geschichte Padé-Näherungsbruch Bibliografie |
url | https://doi.org/10.1007/978-3-642-58169-4 |
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