Essentials of Padé approximants:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York
Acad. Press
1975
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 306 S. graph. Darst. |
| ISBN: | 012074855X |
Staff View
MARC
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| 245 | 1 | 0 | |a Essentials of Padé approximants |c George A. Baker |
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Record in the Search Index
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| adam_text | Titel: Essentials of Padé approximants
Autor: Baker, George A.
Jahr: 1975
Contents
Preface
PARTI ALGEBRAIC PROPERTIES
Chapter 1 Introduction 3
A. The Taylor Series Problem 3
B. Pade Approximants 4
C. Solution for the Pade Approximants 8
D. The Pade Table 9
E. An Application of Pade Approximants to Physics 10
Chapter 2 The Structure of the Pade Table 13
A. The C Table 13
B. Block Structure of the Pade Table 19
C. Existence of Infinitely Many Pade Approximants 24
Chapter 3 Identities 26
A. Two-Term Identities 26
B. Cross Ratios 28
C. Three-Term Identities 30
D. Five-Term Identities 33
E. Three-Term Identity Coefficients from Pade Coefficients 34
F. Compact Expressions for Pade Approximants 36
G. Connection between Fade Tables of/ *) and (1 + ax}f(x} 38
Chapter 4 Relation between Pade Approximants
and Continued Fractions 42
A. Fundamental Recursion Formulas 42
B. Equivalence Transformations 44
C. Convergence Theorems 47
D. Relation of Continued Fractions to Taylor Series 55
E. Relation of Continued Fractions to Pade Approximants 57
F. Bigradients 58
Chapter 5 Gauss s Hypergeometrie Function 62
A. Gauss s Continued Fraction 62
B. Special Cases 64
C. Confluent Hypergeometrie Function 68
D. Bessel Functions 70
E. Divergent Series Derived by Confluence 71
Chapter 6 Recursion Relations 74
A. Classification of Problems 74
B. The Value Problem 75
C. The Coefficient Problem 77
D. The Root Problem 80
Chapter 7 Relation between Orthogonal Polynomials
and Pade Approximants 85
Orthogonality Properties of Fade Denominators 85
Examples from the Classical Orthogonal Polynomial Systems 87
Extremal Properties 89
Decomposition of the Quadratic Form into a Sum of Squares 90
The Eigenvalue Distribution for the Quadratic Form 93
Chapter 8 The iV-Point Pade Approximant 100
General Fade Fitting Problem 100
Determinantal Solution 103
Thiele s Reciprocal Difference Method 105
An Orthogonality Property 106
The Nth Root Fitting Problem 107
Acceleration of the Convergence of a Sequence 108
Chapter 9 Invariance Properties 110
A. Argument Transformations 110
B. Value Transformations 112
C. The Riemann Sphere 113
PART II CONVERGENCE THEORY
Chapter 10 Numerical Examples 121
A. Regular Points 121
B. Singular Points 123
C. Asymptotic Series 127
D. The Location of Cuts 128
E. Noisy Series 131
Chapter 11 Convergence of Vertical and Horizontal Sequences 133
A. Convergence on the Sphere 133
B. Functions with Only Polar Singularities 134
C. Functions with Polar Singularities and
Smooth Nonpolar Singularity 143
D. Several Smooth Boundary Circle Singularities 147
E. Smooth Entire Functions 149
F. Nonvertical Sequences 154
G. General Entire Functions 155
H. The jV-Point Pade Approximants 160
Chapter 12 Convergence of General Sequences 166
A. Continuity on the Sphere 166
B. Convergence Uniqueness Theorem 170
C. Convergence of General Sequences 173
Chapter 13 The Distribution of Poles and Zeros 186
A. The Baker-Ganunel-Wills Conjecture 188
B. Extensions of the Conjectures 188
Chapter 14 Convergence in Hausdorff Measure 193
A. Hausdorff Measure 193
|
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| id | DE-604.BV001957100 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:37:53Z |
| institution | BVB |
| isbn | 012074855X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001275872 |
| oclc_num | 897852 |
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| physical | XI, 306 S. graph. Darst. |
| publishDate | 1975 |
| publishDateSearch | 1975 |
| publishDateSort | 1975 |
| publisher | Acad. Press |
| record_format | marc |
| spelling | Baker, George A. Verfasser aut Essentials of Padé approximants George A. Baker New York Acad. Press 1975 XI, 306 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Padé, Approximation de Padé-benaderingen gtt Padé approximant Padé-Näherungsbruch (DE-588)4173061-6 gnd rswk-swf Padé-Näherung (DE-588)4173060-4 gnd rswk-swf Padé-Näherung (DE-588)4173060-4 s DE-604 Padé-Näherungsbruch (DE-588)4173061-6 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001275872&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Baker, George A. Essentials of Padé approximants Padé, Approximation de Padé-benaderingen gtt Padé approximant Padé-Näherungsbruch (DE-588)4173061-6 gnd Padé-Näherung (DE-588)4173060-4 gnd |
| subject_GND | (DE-588)4173061-6 (DE-588)4173060-4 |
| title | Essentials of Padé approximants |
| title_auth | Essentials of Padé approximants |
| title_exact_search | Essentials of Padé approximants |
| title_full | Essentials of Padé approximants George A. Baker |
| title_fullStr | Essentials of Padé approximants George A. Baker |
| title_full_unstemmed | Essentials of Padé approximants George A. Baker |
| title_short | Essentials of Padé approximants |
| title_sort | essentials of pade approximants |
| topic | Padé, Approximation de Padé-benaderingen gtt Padé approximant Padé-Näherungsbruch (DE-588)4173061-6 gnd Padé-Näherung (DE-588)4173060-4 gnd |
| topic_facet | Padé, Approximation de Padé-benaderingen Padé approximant Padé-Näherungsbruch Padé-Näherung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001275872&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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