Basic hypergeometric series and applications:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[1988]
|
| Schriftenreihe: | Mathematical surveys and monographs
27 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xiii, 124 Seiten |
| ISBN: | 0821815245 |
Internformat
MARC
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| 264 | 4 | |c © 1988 | |
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Datensatz im Suchindex
| _version_ | 1804117895186219008 |
|---|---|
| adam_text | Contents
Foreword ix
Introduction xi
Chapter 1. Fundamental Properties of Basic Hypergeometric Series 1
1. Definitions 1
2. Two functional equations 1
3. The analytic character of F(a, b; t) 2
4. More transformations 2
5. The method of iteration 3
6. Application of iteration (t — tq) 4
7. Iteration of 6 — bq 5
8. Consequences of §7 7
9. Further consequences of §7 8
10. A product series identity 10
11. Iteration of a — aq 12
12. Iteration of (b, t) ? (bq, tq) 13
13. Iteration of (a, t) » (aq, tq) 14
14. Iteration of (a, b, t) —» (aq, bq, tq) 15
15. A Special development 16
16. The partial fraction decomposition 17
17. Jacobi s triple product 18
18. A bilateral series 19
19. Two product series identities 22
20. A general transformation 24
21. The basic multinomial 30
Notes 32
References 35
Chapter 2. Partitions 37
22. Sums over partitions 37
23. Partitions with odd parts and with distinct parts 44
24. Continuation 46
vii
viii CONTENTS
25. The rank of a partition 47
Notes 54
References 54
Chapter 3. Mock Theta Functions and the Functions L(N), J{N) 55
26. Mock theta functions 55
27. The functions L{N) and J(N) 62
Notes 65
References 65
Chapter 4. Other Applications 67
28. Theorems of Liouville type 67
29. Another identity and paraphrase 69
30. Two more identities and their paraphrases 71
31. Sums of Squares 72
32. Products with multiplicative series 77
33. More about products 86
Notes 91
References 92
Chapter 5. Modular Equations 93
34. Modular equations, preliminaries 93
35. A set of functional equations 96
36. Application of (35.13) 97
37. Two modular equations 100
38. Continuation of §36 101
39. Other functional values of H(z) 104
40. A system of identities 107
41. Permanent identities 112
42. Continuation 117
Notes 121
References 122
Bibliography 123
|
| any_adam_object | 1 |
| author | Fine, Nathan J. 1916-1994 |
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| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV003546385 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:01:40Z |
| institution | BVB |
| isbn | 0821815245 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002254137 |
| oclc_num | 260189372 |
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| physical | xiii, 124 Seiten |
| publishDate | 1988 |
| publishDateSearch | 1988 |
| publishDateSort | 1988 |
| publisher | American Mathematical Society |
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| series | Mathematical surveys and monographs |
| series2 | Mathematical surveys and monographs |
| spelling | Fine, Nathan J. 1916-1994 (DE-588)131852841 aut Basic hypergeometric series and applications Providence, Rhode Island American Mathematical Society [1988] © 1988 xiii, 124 Seiten txt rdacontent n rdamedia nc rdacarrier Mathematical surveys and monographs 27 Hypergeometrische Reihe (DE-588)4161061-1 gnd rswk-swf Hypergeometrische Reihe (DE-588)4161061-1 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-1254-8 Mathematical surveys and monographs 27 (DE-604)BV000018014 27 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002254137&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fine, Nathan J. 1916-1994 Basic hypergeometric series and applications Mathematical surveys and monographs Hypergeometrische Reihe (DE-588)4161061-1 gnd |
| subject_GND | (DE-588)4161061-1 |
| title | Basic hypergeometric series and applications |
| title_auth | Basic hypergeometric series and applications |
| title_exact_search | Basic hypergeometric series and applications |
| title_full | Basic hypergeometric series and applications |
| title_fullStr | Basic hypergeometric series and applications |
| title_full_unstemmed | Basic hypergeometric series and applications |
| title_short | Basic hypergeometric series and applications |
| title_sort | basic hypergeometric series and applications |
| topic | Hypergeometrische Reihe (DE-588)4161061-1 gnd |
| topic_facet | Hypergeometrische Reihe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002254137&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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