An introduction to orthogonal polynomials:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Gordon and Breach
1978
|
| Series: | Mathematics and its applications
13 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 249 S. graph. Darst. |
| ISBN: | 0677041500 |
Staff View
MARC
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| 245 | 1 | 0 | |a An introduction to orthogonal polynomials |c T. S. Chihara |
| 264 | 1 | |a New York [u.a.] |b Gordon and Breach |c 1978 | |
| 300 | |a XII, 249 S. |b graph. Darst. | ||
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| 490 | 1 | |a Mathematics and its applications |v 13 | |
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| 650 | 7 | |a Orthogonale reeksen |2 gtt | |
| 650 | 4 | |a Functions, Orthogonal | |
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Record in the Search Index
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| adam_text | Contents
PREFACE vii
CHAPTER I. ELEMENTARY THEORY OF ORTHOGONAL POLYNOMIALS 1
1 Introduction 1
2 The moment functional and orthogonality 6
3 Existence of OPS 11
4 The fundamental recurrence formula 18
5 Zeros 26
6 Gauss quadrature 31
7 Kernel polynomials 35
8 Symmetric moment functionals 40
9 Certain related recurrence relations 45
CHAPTER II. THE REPRESENTATION THEOREM AND DISTRIBUTION
FUNCTIONS 51
1 Introduction 51
2 Some preliminary theorems 52
3 The representation theorem 56
4 Spectral points and zeros of orthogonal polynomials 59
5 Determinacy of £ in the bounded case 63
6 The classical moment problems 71
CHAPTER III. CONTINUED FRACTIONS AND CHAIN SEQUENCES 77
1 Basic concepts 77
2 The fundamental recurrence formulas 80
3 A convergence theorem 82
4 Jacobi fractions and orthogonal polynomials 85
5 Chain sequences 91
6 Additional results on chain sequences 100
xi
Xil AN INTRODUCTION TO ORTHOGONAL POLYNOMIALS
CHAPTER IV. THE RECURRENCE FORMULA AND PROPERTIES OF
ORTHOGONAL POLYNOMIALS 107
1 Introduction 107
2 Chain sequences and orthogonal polynomials 108
3 Some spectral analysis 113
4 OPS whose zeros are dense in intervals 120
5 Preliminaries to Krein s theorem 128
6 Krein s theorem 133
CHAPTER V. SPECIAL FUNCTIONS 142
1 General remarks 142
2 The classical orthogonal polynomials 142
3 The Hahn class of orthogonal polynomials 159
4 The Meixner class of orthogonal polynomials 163
5 Other classes of orthogonal polynomials 166
CHAPTER VI. SOME SPECIFIC SYSTEMS OF ORTHOGONAL POLYNOMIALS.. 170
1 The Charlier polynomials 170
2 The Stieltjes Wigert polynomials 172
3 The Meixner polynomials 175
4 The Bessel polynomials 181
5 The Pollaczek polynomials 184
6 Modified Lommel polynomials 187
7 Tricomi Carlitz polynomials 190
8 OPS related to Bernoulli numbers 191
9 OPS related to Jacobi elliptic functions 193
10 The ^ polynomials of Al Salam and Carlitz 195
11 Wall polynomials 198
12 Associated Legendre polynomials 201
13 Miscellaneous OPS 203
notes 209
appendix table of recurrence formulas 215
list of frequently used symbols 223
bibliography 225
INDEX 243
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T15:42:49Z |
| institution | BVB |
| isbn | 0677041500 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001480531 |
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| physical | XII, 249 S. graph. Darst. |
| publishDate | 1978 |
| publishDateSearch | 1978 |
| publishDateSort | 1978 |
| publisher | Gordon and Breach |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Chihara, Theodore S. Verfasser aut An introduction to orthogonal polynomials T. S. Chihara New York [u.a.] Gordon and Breach 1978 XII, 249 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 13 Fonctions orthogonales Orthogonale reeksen gtt Functions, Orthogonal Orthogonale Polynome (DE-588)4172863-4 gnd rswk-swf Orthogonale Polynome (DE-588)4172863-4 s DE-604 Mathematics and its applications 13 (DE-604)BV008163334 13 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001480531&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Chihara, Theodore S. An introduction to orthogonal polynomials Mathematics and its applications Fonctions orthogonales Orthogonale reeksen gtt Functions, Orthogonal Orthogonale Polynome (DE-588)4172863-4 gnd |
| subject_GND | (DE-588)4172863-4 |
| title | An introduction to orthogonal polynomials |
| title_auth | An introduction to orthogonal polynomials |
| title_exact_search | An introduction to orthogonal polynomials |
| title_full | An introduction to orthogonal polynomials T. S. Chihara |
| title_fullStr | An introduction to orthogonal polynomials T. S. Chihara |
| title_full_unstemmed | An introduction to orthogonal polynomials T. S. Chihara |
| title_short | An introduction to orthogonal polynomials |
| title_sort | an introduction to orthogonal polynomials |
| topic | Fonctions orthogonales Orthogonale reeksen gtt Functions, Orthogonal Orthogonale Polynome (DE-588)4172863-4 gnd |
| topic_facet | Fonctions orthogonales Orthogonale reeksen Functions, Orthogonal Orthogonale Polynome |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001480531&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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