Special functions for engineers and applied mathematicians:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York
Macmillan
1985
|
| Ausgabe: | 1. print. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VIII, 357 S. graph. Darst. |
| ISBN: | 0029486505 |
Internformat
MARC
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| 100 | 1 | |a Andrews, Larry C. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Special functions for engineers and applied mathematicians |
| 250 | |a 1. print. | ||
| 264 | 1 | |a New York |b Macmillan |c 1985 | |
| 300 | |a VIII, 357 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Fonctions spéciales | |
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Datensatz im Suchindex
| _version_ | 1804118033581473792 |
|---|---|
| adam_text | Contents
Preface vii
1 INFINITE SERIES, IMPROPER INTEGRALS, AND
INFINITE PRODUCTS 1
1.1 Introduction 1
1.2 Infinite Series of Constants 2
1.3 Infinite Series of Functions 15
1.4 Asymptotic Series 26
1.5 Fourier Trigonometric Series 32
1.6 Improper Integrals 38
1.7 Infinite Products 45
2 THE GAMMA FUNCTION AND
RELATED FUNCTIONS 50
2.1 Introduction 50
2.2 Gamma Function 51
2.3 Beta Function 66
2.4 Incomplete Gamma Function 71
2.5 Digamma and Polygamma Functions 74
3 OTHER FUNCTIONS DEFINED BY INTEGRALS 92
3.1 Introduction 92
3.2 The Error Function and Related Functions 93
iii
iv • Special Functions for Engineers and Applied Mathematicians
3.3 The Exponential Integral and Related Functions 103
3.4 Elliptic Integrals 108
4 LEGENDRE POLYNOMIALS AND
RELATED FUNCTIONS 116
4.1 Introduction 116
4.2 The Generating Function 117
4.3 Other Representations of the Legendre Polynomials 132
4.4 Legendre Series 137
4.5 Convergence of the Series 147
4.6 Legendre Functions of the Second Kind 155
4.7 Associated Legendre Functions 160
5 OTHER ORTHOGONAL POLYNOMIALS 166
5.1 Introduction 166
5.2 Hermite Polynomials 167
5.3 Laguerre Polynomials 176
5.4 Generalized Polynomial Sets 184
6 BESSEL FUNCTIONS 195
6.1 Introduction 195
6.2 Bessel Functions of the First Kind 196
6.3 Integral Representations and Integrals of Bessel Functions 205
6.4 Bessel Series 215
6.5 Bessel Functions of the Second and Third Kinds 220
6.6 Differential Equations Related to Bessel s Equation 228
6.7 Modified Bessel Functions 232
6.8 Other Bessel Functions 241
6.9 Asymptotic Formulas 248
7 BOUNDARY VALUE PROBLEMS 252
7.1 Introduction 252
7.2 Spherical Domains: Legendre Functions 253
7.3 Circular and Cylindrical Domains: Bessel Functions 264
8 THE HYPERGEOMETRIC FUNCTION 272
8.1 Introduction 272
8.2 The Pochhammer Symbol 273
8.3 The Function F(a, b; c; x) 276
Contents • v
8.4 Relation to Other Functions 285
8.5 Summing Series 292
9 THE CONFLUENT HYPERGEOMETRIC FUNCTION 298
9.1 Introduction 298
9.2 The Functions M(a;c;x) and U(a;c;x) 299
9.3 Relation to Other Functions 308
9.4 Whittaker Functions 315
10 GENERALIZED HYPERGEOMETRIC FUNCTIONS 321
10.1 Introduction 321
10.2 The Set of Functions pFq 322
10.3 Other Generalizations 327
BIBLIOGRAPHY 333
APPENDIX: A LIST OF SPECIAL FUNCTION FORMULAS 335
SELECTED ANSWERS TO EXERCISES 348
INDEX 351
|
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
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| dewey-search | 515/.5 515.9 |
| dewey-sort | 3515 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. print. |
| format | Book |
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| id | DE-604.BV003689722 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:03:52Z |
| institution | BVB |
| isbn | 0029486505 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002347711 |
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| owner_facet | DE-384 DE-824 |
| physical | VIII, 357 S. graph. Darst. |
| publishDate | 1985 |
| publishDateSearch | 1985 |
| publishDateSort | 1985 |
| publisher | Macmillan |
| record_format | marc |
| spelling | Andrews, Larry C. Verfasser aut Special functions for engineers and applied mathematicians 1. print. New York Macmillan 1985 VIII, 357 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Fonctions spéciales Functions, Special Spezielle Funktion (DE-588)4182213-4 gnd rswk-swf Spezielle Funktion (DE-588)4182213-4 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002347711&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Andrews, Larry C. Special functions for engineers and applied mathematicians Fonctions spéciales Functions, Special Spezielle Funktion (DE-588)4182213-4 gnd |
| subject_GND | (DE-588)4182213-4 |
| title | Special functions for engineers and applied mathematicians |
| title_auth | Special functions for engineers and applied mathematicians |
| title_exact_search | Special functions for engineers and applied mathematicians |
| title_full | Special functions for engineers and applied mathematicians |
| title_fullStr | Special functions for engineers and applied mathematicians |
| title_full_unstemmed | Special functions for engineers and applied mathematicians |
| title_short | Special functions for engineers and applied mathematicians |
| title_sort | special functions for engineers and applied mathematicians |
| topic | Fonctions spéciales Functions, Special Spezielle Funktion (DE-588)4182213-4 gnd |
| topic_facet | Fonctions spéciales Functions, Special Spezielle Funktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002347711&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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