Special functions of mathematical physics and chemistry:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London
Longman
1980
|
| Ausgabe: | 3. ed. |
| Schriftenreihe: | Longman mathematical texts.
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX, 182 S. |
| ISBN: | 0582443962 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804121845622898688 |
|---|---|
| adam_text | Contents
Preface v
1: Introduction 1
§1 The origin of special functions 1
§2 Solution in series of linear differential equations 4
2.1 Ordinary points of a linear differential equation 4
2.2 Regular singular points 6
2.3 The point at infinity 8
§3 Solution in form of a contour integral 8
3.1 The Fourier Laplace method 9
3.2 The Euler method 12
§4 Self adjoint linear equations of the second order 16
4.1 Separation and comparison theorems 16
4.2 Eigenvalues and eigenfunctions 18
§5 The gamma function and related functions 21
Problems I 25
2: Hypergeometric functions 34
§6 The hypergeometric series 34
§7 An integral formula for the hypergeometric series 36
§8 The hypergeometric equation 39
§9 Linear relations between the solutions of the
hypergeometric function 46
§10 Relations of contiguity 48
§11 The confluent hypergeometric function 49
§12 Generalised hypergeometric series 53
Problems II 56
3: Legendre functions 63
§13 Legendre polynomials 63
viii Contents
§14 Recurrence relations for the Legendre polynomials 68
§15 The formulae of Murphy and Rodrigues 69
§16 Series of Legendre polynomials 72
§17 Legendre s differential equation 74
§18 Neumann s formula for the Legendre functions 77
§19 Recurrence relations for the function Qn(/x) 81
§20 The use of Legendre functions in potential theory 82
§21 Legendre s associated functions 85
§22 Integral expression for the associated Legendre function 90
§23 Surface spherical harmonics 92
§24 Use of associated Legendre functions in wave mechanics 94
Problems III 96
4: Bessel functions 106
§25 The origin of Bessel functions 106
§26 Recurrence relations for the Bessel coefficients 109
§27 Series expansion for the Bessel coefficients 111
§28 Integral expressions for the Bessel coefficients 114
§29 The addition formula for the Bessel coefficients 115
§30 Bessel s differential equation 117
§31 Spherical Bessel functions 121
§32 Integrals involving Bessel functions 123
§33 The modified Bessel functions 127
§34 The Ber and Bei functions 130
§35 Expansions in series of Bessel functions 132
§36 The use of Bessel functions in potential theory 134
§37 Asymptotic expansions of Bessel functions 137
Problems IV 140
5: The functions of Hermite and Laguerre 148
§38 The Hermite polynomials 148
§39 Hermite s differential equation 150
§40 Hermite functions 152
§41 The occurrence of Hermite functions in wave mechanics 155
§42 The Laguerre polynomials 157
§43 Laguerre s differential equation 161
§44 The associated Laguerre polynomials and functions 162
Contents ix
§45 The wave functions for the hydrogen atom 164
Problems V 168
6: Appendix 175
§46 The Dirac delta function 175
References 179
Index 180
|
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| author | Sneddon, Ian Naismith 1919-2000 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 3. ed. |
| format | Book |
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| isbn | 0582443962 |
| language | English |
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| physical | IX, 182 S. |
| publishDate | 1980 |
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| publisher | Longman |
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| series2 | Longman mathematical texts. |
| spelling | Sneddon, Ian Naismith 1919-2000 Verfasser (DE-588)121675343 aut Special functions of mathematical physics and chemistry 3. ed. London Longman 1980 IX, 182 S. txt rdacontent n rdamedia nc rdacarrier Longman mathematical texts. Fonctions spéciales Functions, Special Funktion Mathematik (DE-588)4071510-3 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Chemie (DE-588)4009816-3 gnd rswk-swf Spezielle Funktion (DE-588)4182213-4 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Funktion (DE-588)4195664-3 gnd rswk-swf 1\p (DE-588)4155008-0 Formelsammlung gnd-content Mathematik (DE-588)4037944-9 s Chemie (DE-588)4009816-3 s Funktion (DE-588)4195664-3 s DE-604 Mathematische Physik (DE-588)4037952-8 s Spezielle Funktion (DE-588)4182213-4 s 2\p DE-604 Funktion Mathematik (DE-588)4071510-3 s 3\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004919289&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Sneddon, Ian Naismith 1919-2000 Special functions of mathematical physics and chemistry Fonctions spéciales Functions, Special Funktion Mathematik (DE-588)4071510-3 gnd Mathematik (DE-588)4037944-9 gnd Chemie (DE-588)4009816-3 gnd Spezielle Funktion (DE-588)4182213-4 gnd Mathematische Physik (DE-588)4037952-8 gnd Funktion (DE-588)4195664-3 gnd |
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| title | Special functions of mathematical physics and chemistry |
| title_auth | Special functions of mathematical physics and chemistry |
| title_exact_search | Special functions of mathematical physics and chemistry |
| title_full | Special functions of mathematical physics and chemistry |
| title_fullStr | Special functions of mathematical physics and chemistry |
| title_full_unstemmed | Special functions of mathematical physics and chemistry |
| title_short | Special functions of mathematical physics and chemistry |
| title_sort | special functions of mathematical physics and chemistry |
| topic | Fonctions spéciales Functions, Special Funktion Mathematik (DE-588)4071510-3 gnd Mathematik (DE-588)4037944-9 gnd Chemie (DE-588)4009816-3 gnd Spezielle Funktion (DE-588)4182213-4 gnd Mathematische Physik (DE-588)4037952-8 gnd Funktion (DE-588)4195664-3 gnd |
| topic_facet | Fonctions spéciales Functions, Special Funktion Mathematik Mathematik Chemie Spezielle Funktion Mathematische Physik Funktion Formelsammlung |
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