History of continued fractions and Padé approximants:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1991
|
| Series: | Springer series in computational mathematics
12 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 347 - 492 |
| Physical Description: | 551 S. graph. Darst. |
| ISBN: | 3540152865 0387152865 |
Staff View
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Record in the Search Index
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|---|---|
| adam_text | Contents
INTRODUCTION 1
CHAPTER 1
THE EARLY AGES 3
1.1 Euclid s algorithm 3
1.2 The square root 9
1.3 Indeterminate equations 28
1.4 History of notations 44
CHAPTER 2
THE FIRST STEPS 51
2.1 Ascending continued fractions 51
2.2 The birth of continued fractions 61
2.3 Miscellaneous contributions 70
2.4 Pell s equation 72
CHAPTER 3
THE BEGINNING OF THE THEORY 77
3.1 Brouncker and Wallis 77
3.2 Huygens 86
3.3 Number theory 92
CHAPTER 4
GOLDEN AGE 97
4.1 Euler 97
4.2 Lambert 109
4.3 Lagrange 112
4.4 Miscellaneous contributions 125
4.5 The birth of Pade approximants 128
CHAPTER 5
MATURITY 141
5.1 Arithmetical continued fractions 142
5.1.1 Algebraic properties 142
5.1.2 Arithmetic 145
5.1.3 Applications 160
5.1.4 Number theory 171
5.1.5 Convergence 187
5.2 Algebraic continued fractions 190
5.2.1 Expansion methods and properties 190
5.2.2 Examples and applications 193
5.2.3 Orthogonal polynomials 213
5.2.4 Convergence and analytic theory 224
5.2.5 Pade approximants 236
5.3 Varia 255
CHAPTER 6
THE MODERN TIMES 261
6.1 Number theory 261
6.2 Set and probability theories 272
6.3 Convergence and analytic theory 284
6.4 Pade approximants 292
6.5 Extensions and applications 301
APPENDIX 313
DOCUMENTS 313
Document 1: L algebre des geometres grecs 314
Document 2: Histoire de l Academie Royale des Sciences . 320
Document 3: Encyclopedic (Supplement) 324
Document 4: Elementary Mathematics from an advanced
standpoint 326
Document 5: Sur quelques applications des fractions continues 329
Document 6: Rapport sur un Memoire de M. Stieltjes . . . 335
Document 7: Correspondance d Hermite et de Stieltjes . . 337
Document 8: Notice sur les travaux et titres 338
Document 9: Note annexe sur les fractions continues . . . 345
SCIENTIFIC BIBLIOGRAPHY 347
WORKS 463
HISTORICAL BIBLIOGRAPHY 469
NAME INDEX 493
SUBJECT INDEX 547
|
| any_adam_object | 1 |
| author | Brezinski, Claude 1941- |
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| classification_tum | MAT 415f |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| era | Geschichte Anfänge-1939 gnd |
| era_facet | Geschichte Anfänge-1939 |
| format | Book |
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| indexdate | 2024-07-09T16:11:30Z |
| institution | BVB |
| isbn | 3540152865 0387152865 |
| language | English |
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| physical | 551 S. graph. Darst. |
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| series | Springer series in computational mathematics |
| series2 | Springer series in computational mathematics |
| spelling | Brezinski, Claude 1941- Verfasser (DE-588)108764737 aut History of continued fractions and Padé approximants Claude Brezinski Berlin [u.a.] Springer 1991 551 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer series in computational mathematics 12 Literaturverz. S. 347 - 492 Geschichte Anfänge-1939 gnd rswk-swf Fractions continues ram Continued fractions Padé approximant Bibliografie (DE-588)4006432-3 gnd rswk-swf Kettenbruch (DE-588)4030401-2 gnd rswk-swf Padé-Näherungsbruch (DE-588)4173061-6 gnd rswk-swf Geschichte (DE-588)4020517-4 gnd rswk-swf Kettenbruch (DE-588)4030401-2 s Geschichte Anfänge-1939 z DE-604 Padé-Näherungsbruch (DE-588)4173061-6 s Bibliografie (DE-588)4006432-3 s Geschichte (DE-588)4020517-4 s Springer series in computational mathematics 12 (DE-604)BV000012004 12 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002689508&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Brezinski, Claude 1941- History of continued fractions and Padé approximants Springer series in computational mathematics Fractions continues ram Continued fractions Padé approximant Bibliografie (DE-588)4006432-3 gnd Kettenbruch (DE-588)4030401-2 gnd Padé-Näherungsbruch (DE-588)4173061-6 gnd Geschichte (DE-588)4020517-4 gnd |
| subject_GND | (DE-588)4006432-3 (DE-588)4030401-2 (DE-588)4173061-6 (DE-588)4020517-4 |
| 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 Claude Brezinski |
| title_fullStr | History of continued fractions and Padé approximants Claude Brezinski |
| title_full_unstemmed | History of continued fractions and Padé approximants Claude Brezinski |
| title_short | History of continued fractions and Padé approximants |
| title_sort | history of continued fractions and pade approximants |
| topic | Fractions continues ram Continued fractions Padé approximant Bibliografie (DE-588)4006432-3 gnd Kettenbruch (DE-588)4030401-2 gnd Padé-Näherungsbruch (DE-588)4173061-6 gnd Geschichte (DE-588)4020517-4 gnd |
| topic_facet | Fractions continues Continued fractions Padé approximant Bibliografie Kettenbruch Padé-Näherungsbruch Geschichte |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002689508&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000012004 |
| work_keys_str_mv | AT brezinskiclaude historyofcontinuedfractionsandpadeapproximants |