Special functions for scientists and engineers:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London u.a.
Van Nostrand
1968
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 247 S. graph. Darst. |
Internformat
MARC
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| 245 | 1 | 0 | |a Special functions for scientists and engineers |c W. W. Bell |
| 264 | 1 | |a London u.a. |b Van Nostrand |c 1968 | |
| 300 | |a XIV, 247 S. |b graph. Darst. | ||
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| 650 | 4 | |a Fonctions spéciales | |
| 650 | 4 | |a Functions, Special | |
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Datensatz im Suchindex
| _version_ | 1804118306916925440 |
|---|---|
| adam_text | CONTENTS
Preface v
List of Symbols ix
Chapter 1 Series Solution of Differential Equations
1.1 Method of Frobenius 1
1.2 Examples 8
Problems 21
Chapter 2 Gamma and Beta Functions
2.1 Definitions 23
2.2 Properties of the beta and gamma functions 24
2.3 Definition of the gamma function for negative values of the
argument 30
2.4 Examples 37
Problems 40
Chapter 3 Legendre Polynomials and Functions
3.1 Legendre s equation and its solution 42
3.2 Generating function for the Legendre polynomials 46
3.3 Further expressions for the Legendre polynomials 48
3.4 Explicit expressions for and special values of the Legendre
polynomials 50
3.5 Orthogonality properties of the Legendre polynomials 52
3.6 Legendre series 55
3.7 Relations between the Legendre polynomials and their deriva¬
tives; recurrence relations 58
3.8 Associated Legendre functions 62
3.9 Properties of the associated Legendre functions 65
3.10 Legendre functions of the second kind 70
3.11 Spherical harmonics 78
3.12 Graphs of the Legendre functions 82
3.13 Examples 85
Problems 90
xii CONTENTS
Chapter 4 Bessel Functions
4.1 Bessel s equation and its solutions; Bessel functions of the first
and second kind 92
4.2 Generating function for the Bessel functions 99
4.3 Integral representations for Bessel functions 101
4.4 Recurrence relations 104
4.5 Hankel functions 107
4.6 Equations reducible to Bessel s equation 108
4.7 Modified Bessel functions 110
4.8 Recurrence relations for the modified Bessel functions 113
4.9 Integral representations for the modified Bessel functions 116
4.10 Kelvin s functions 120
4.11 Spherical Bessel functions 121
4.12 Behaviour of the Bessel functions for large and small values of
the argument 127
4.13 Graphs of the Bessel functions 133
4.14 Orthonormality of the Bessel functions; Bessel series 137
4.15 Integrals involving Bessel functions 141
4.16 Examples 148
Problems 154
Chapter 5 Hermite Polynomials
5.1 Hermite s equation and its solution 156
5.2 Generating function 157
5.3 Other expressions for the Hermite polynomials 158
5.4 Explicit expressions for, and special values of, the Hermite
polynomials 160
5.5 Orthogonality properties of the Hermite polynomials 161
5.6 Relations between Hermite polynomials and their derivatives;
recurrence relations 162
5.7 Weber Hermite functions 163
5.8 Examples 164
Problems 166
Chapter 6 Laguerre Polynomials
6.1 Laguerre s equation and its solution 168
6.2 Generating function 169
6.3 Alternative expression for the Laguerre polynomials 170
6.4 Explicit expressions for, and special values of, the Laguerre
polynomials 171
CONTENTS xiii
6.5 Orthogonality properties of the Laguerre polynomials 172
6.6 Relations between Laguerre polynomials and their derivatives;
recurrence relations 173
6.7 Associated Laguerre polynomials 176
6.8 Properties of the associated Laguerre polynomials 177
6.9 Notation 182
6.10 Examples 182
Problems 185
Chapter 7 Chebyshev Polynomials
7.1 Definition of Chebyshev polynomials; Chebyshev s equation 187
7.2 Generating function 190
7.3 Orthogonality properties 192
7.4 Recurrence relations 193
7.5 Examples 194
Problems 196
Chapter 8 Gegenbauer and Jacobi Polynomials
8.1 Gegenbauer polynomials 197
8.2 Jacobi polynomials 198
8.3 Examples 200
Problems 201
Chapter 9 Hypergeometric Functions
9.1 Definition of hypergeometric functions 203
9.2 Properties of the hypergeometric function 207
9.3 Properties of the confluent hypergeometric function 210
9.4 Examples 212
Problems 216
Chapter 10 Other Special Functions
10.1 Incomplete gamma functions 218
10.2 Exponential integral and related functions 218
10.3 The error function and related functions 221
10.4 Riemann s zeta function 223
10.5 Debye functions 224
10.6 Elliptic integrals 224
10.7 Examples 225
Problems 228
xiv CONTENTS
Appendices
1 Convergence of Legendre series 230
2 Euler s constant 231
3 Differential equations 233
4 Orthogonality relations 234
5 Generating functions 236
Hints and Solutions to Problems 237
Bibliography 243
Index 245
|
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| indexdate | 2024-07-09T16:08:13Z |
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| language | English |
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| physical | XIV, 247 S. graph. Darst. |
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| spelling | Bell, William W. Verfasser aut Special functions for scientists and engineers W. W. Bell London u.a. Van Nostrand 1968 XIV, 247 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=002549157&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bell, William W. Special functions for scientists and engineers Fonctions spéciales Functions, Special Spezielle Funktion (DE-588)4182213-4 gnd |
| subject_GND | (DE-588)4182213-4 |
| title | Special functions for scientists and engineers |
| title_auth | Special functions for scientists and engineers |
| title_exact_search | Special functions for scientists and engineers |
| title_full | Special functions for scientists and engineers W. W. Bell |
| title_fullStr | Special functions for scientists and engineers W. W. Bell |
| title_full_unstemmed | Special functions for scientists and engineers W. W. Bell |
| title_short | Special functions for scientists and engineers |
| title_sort | special functions for scientists and engineers |
| topic | Fonctions spéciales Functions, Special Spezielle Funktion (DE-588)4182213-4 gnd |
| topic_facet | Fonctions spéciales Functions, Special Spezielle Funktion |
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