Orthogonal polynomials and continued fractions: from Euler's point of view
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge University Press
2008
|
| Ausgabe: | 1. publication |
| Schriftenreihe: | Encyclopedia of Mathematics and Its Applications
122 |
| Schlagworte: | |
| Online-Zugang: | kostenfrei Zentralblatt MATH Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XVI, 478 Seiten graph. Darst. 25 cm |
| ISBN: | 0521854199 9780521854191 |
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| 245 | 1 | 0 | |a Orthogonal polynomials and continued fractions |b from Euler's point of view |c Sergey Khrushchev, Atilim University, Turkey |
| 250 | |a 1. publication | ||
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| 650 | 0 | |a Continued fractions | |
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| 650 | 4 | |a Continued fractions | |
| 650 | 4 | |a Orthogonal polynomials | |
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Datensatz im Suchindex
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| adam_text | ORTHOGONAL POLYNOMIALS AND CONTINUED FRACTIONS FROM EULER S POINT OF
VIEW SERGEY KHRUSHCHEV ATILIM UNIVERSITY, TURKEY CAMBRIDGE UNIVERSITY
PRESS CONTENTS PREFACE * PAGE IX CONTINUED FRACTIONS: REAL NUMBERS 1 1.1
HISTORICAL BACKGROUND 1 1.2 EULER S THEORY OF CONTINUED FRACTIONS 11 1.3
RATIONAL APPROXIMATIONS 17 1.4 JEAN BERNOULLI SEQUENCES 36 1.5 MARKOFF
SEQUENCES 49 CONTINUED FRACTIONS: ALGEBRA 71 2.1 EULER S ALGORITHM 71
2.2 LAGRANGE S THEOREM 81 2.3 PELL S EQUATION * 84 2.4 EQUIVALENT
IRRATIONALS 92 2.5 MARKOFF S THEORY 98 CONTINUED FRACTIONS: ANALYSIS 123
3.1 CONVERGENCE: ELEMENTARY METHODS 123 3.2 CONTRIBUTION OF BROUNCKER
AND WALLIS 131 3.3 BROUNCKER S METHOD AND THE GAMMA FUNCTION 146
CONTINUED FRACTIONS: EULER 158 4.1 PARTIAL SUMS 158 4.2 EULER S VERSION
OF BROUNCKER S-METHOD * * 163 4.3 AN EXTENSION OF WALLIS FORMULA , 169
4.4 WALLIS FORMULA FOR SINUSOIDAL SPIRALS 174 4.5 AN EXTENSION OF
BROUNCKER S FORMULA 177 4.6 ON THE FORMATION OF CONTINUED FRACTIONS 180
4.7 EULER S DIFFERENTIAL METHOD 183 4.8 LAPLACE TRANSFORM OF HYPERBOLIC
SECANT 191 4.9 STIELTJES CONTINUED FRACTIONS 194 4.10 CONTINUED
FRACTION OF HYPERBOLIC COTANGENT 199 4.11 RICCATI S EQUATION 206 VN VIII
CONTENTS CONTINUED FRACTIONS: EULER S INFLUENCE 5.1 5.2 5.3 5.4
BAUER-MUIR-PERRON THEORY FROM EULER TO SCOTT-WALL THE IRRATIONALITY OF
TT THE PARABOLA THEOREM P-FRACTIONS 6.1 6.2 6.3 6.4 6.5 LAURENT SERIES
CONVERGENTS QUADRATIC IRRATIONALS HYPERGEOMETRIC SERIES STIELTJES
THEORY ORTHOGONAL POLYNOMIALS 7.1 7.2 7.3 7.4 7.5 EULER S PROBLEM
QUADRATURE FORMULAS STURM S METHOD CHEBYSHEV S APPROACH TO ORTHOGONAL
POLYNOMIALS EXAMPLES OF ORTHOGONAL POLYNOMIALS ORTHOGONAL POLYNOMIALS ON
THE UNIT CIRCLE . , 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9 8.10 8.11
ORTHOGONAL POLYNOMIALS AND CONTINUED FRACTIONS THE GRAM-SCHMIDT
ALGORITHM SZEGS S ALTERNATIVE ERDOS MEASURES THE CONTINUUM OF SCHUR
PARAMETERS RAKHMANOV MEASURES CONVERGENCE OF SCHUR S ALGORITHM ON T
NEVAI S CLASS INNER FUNCTIONS AND SINGULAR MEASURES SCHUR FUNCTIONS OF
SMOOTH MEASURES PERIODIC MEASURES * I APPENDIX CONTINUED FRACTIONS,
OBSERVATIONS L. EULER (1739) : REFERENCES INDEX 228 229 232 238 240 247
247 253 258 272 285 296 296 298 303 310 315 . ** 322 ; 322 336 346 356
360 364 368 371 380 388 390 426 ; 466 475
|
| any_adam_object | 1 |
| author | Khrushchev, Sergei 1935-2020 |
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| classification_rvk | SK 470 SK 680 |
| classification_tum | MAT 330f MAT 430f MAT 410f |
| ctrlnum | (OCoLC)474173492 (DE-599)GBV566061538 |
| discipline | Mathematik |
| edition | 1. publication |
| format | Book |
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| indexdate | 2024-07-09T21:53:19Z |
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| isbn | 0521854199 9780521854191 |
| language | English |
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| physical | XVI, 478 Seiten graph. Darst. 25 cm |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Cambridge University Press |
| record_format | marc |
| series | Encyclopedia of Mathematics and Its Applications |
| series2 | Encyclopedia of Mathematics and Its Applications |
| spelling | Khrushchev, Sergei 1935-2020 Verfasser (DE-588)123601703 aut Orthogonal polynomials and continued fractions from Euler's point of view Sergey Khrushchev, Atilim University, Turkey 1. publication Cambridge [u.a.] Cambridge University Press 2008 XVI, 478 Seiten graph. Darst. 25 cm txt rdacontent n rdamedia nc rdacarrier Encyclopedia of Mathematics and Its Applications 122 Includes bibliographical references and index Euler, Leonhard / 1707-1783 Euler, Leonhard <1707-1783> Euler, Leonhard 1707-1783 (DE-588)118531379 gnd rswk-swf Orthogonal polynomials Continued fractions Matematisk analyse Orthogonale Polynome (DE-588)4172863-4 gnd rswk-swf Kettenbruch (DE-588)4030401-2 gnd rswk-swf Euler, Leonhard 1707-1783 (DE-588)118531379 p Orthogonale Polynome (DE-588)4172863-4 s Kettenbruch (DE-588)4030401-2 s DE-604 Encyclopedia of Mathematics and Its Applications 122 (DE-604)BV000903719 122 http://www.gbv.de/dms/goettingen/566061538.pdf kostenfrei Inhaltsverzeichnis DE-601 pdf/application http://www.zentralblatt-math.org/zmath/en/search/?an=1151.33002 Zentralblatt MATH kostenfrei Inhaltstext GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018012531&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Khrushchev, Sergei 1935-2020 Orthogonal polynomials and continued fractions from Euler's point of view Encyclopedia of Mathematics and Its Applications Euler, Leonhard / 1707-1783 Euler, Leonhard <1707-1783> Euler, Leonhard 1707-1783 (DE-588)118531379 gnd Orthogonal polynomials Continued fractions Matematisk analyse Orthogonale Polynome (DE-588)4172863-4 gnd Kettenbruch (DE-588)4030401-2 gnd |
| subject_GND | (DE-588)118531379 (DE-588)4172863-4 (DE-588)4030401-2 |
| title | Orthogonal polynomials and continued fractions from Euler's point of view |
| 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, Atilim University, Turkey |
| title_fullStr | Orthogonal polynomials and continued fractions from Euler's point of view Sergey Khrushchev, Atilim University, Turkey |
| title_full_unstemmed | Orthogonal polynomials and continued fractions from Euler's point of view Sergey Khrushchev, Atilim University, Turkey |
| 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> Euler, Leonhard 1707-1783 (DE-588)118531379 gnd Orthogonal polynomials Continued fractions Matematisk analyse Orthogonale Polynome (DE-588)4172863-4 gnd Kettenbruch (DE-588)4030401-2 gnd |
| topic_facet | Euler, Leonhard / 1707-1783 Euler, Leonhard <1707-1783> Euler, Leonhard 1707-1783 Orthogonal polynomials Continued fractions Matematisk analyse Orthogonale Polynome Kettenbruch |
| url | http://www.gbv.de/dms/goettingen/566061538.pdf http://www.zentralblatt-math.org/zmath/en/search/?an=1151.33002 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018012531&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000903719 |
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