Mathieu functions and spheroidal functions and their mathematical foundations: further studies
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1980
|
| Series: | Lecture notes in mathematics
837 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VII, 126 S. |
| ISBN: | 3540102825 0387102825 |
Staff View
MARC
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| 240 | 1 | 0 | |a Mathieusche Funktionen und Sphäroidfunktionen |
| 245 | 1 | 0 | |a Mathieu functions and spheroidal functions and their mathematical foundations |b further studies |c Josef Meixner ; Friedrich Wilhelm Schäfke ; Gerhard Wolf |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1980 | |
| 300 | |a VII, 126 S. | ||
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| 490 | 1 | |a Lecture notes in mathematics |v 837 | |
| 650 | 4 | |a Fonctions sphéroïdales | |
| 650 | 4 | |a Mathieu, Fonctions de | |
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Record in the Search Index
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| adam_text | TABLE OF CONTENTS
Introduction and Preface.
I. Foundations.
1.1. Eigenvalue problems with two parameters. 1
1.1.0. Introduction. 1
1.1.1. First presuppositions. Preliminary remarks. 3
1.1.2. Estimates for the resolvent. 7
1.1.3 The eigenvalues to y * 0. 11
1.1.4. Further presuppositions and conclusions 15
1.1.5. The residues of the resolvent. Principal solutions. 16
1.1.6. Equiconvergence. 22
1.1.7 Holomorphy properties. Estimates. 23
1.1.8. Additional estimates. 26
1.1.9. On the application to boundary value problems for ordinary 27
differential equations and differential systems.
1.1.10. Application to Hill s differential equation in the real 33
doma i n.
1.1.11. Application to Hill s differential equation in the complex 36
doma i n.
1.1.12. Application to the spheroidal differential equation in the 39
real domain.
1.1.13. Application to the spheroidal differential equation in the 42
complex domain.
1.2. Simply separated operators. 44
1.2.0. Introduction. 44
1.2.1. The algebraic problem. 46
1.2.2. Adjoint mappings. 50
1.2.3. The analytical problem. Expansion theorem. 53
1.2.4. The symmetric case. 58
1.2.5. Applications. 60
2. Mathieu Functions. 63
2.1. Integral relations. 63
2.1.1. Integral relations of the first kind. 63
2.1.2. Integral relations of the second kind (with variable 71
boundaries).
IV
2.2. Addition theorems. 73
2.2.1. Lemmas concerning the transformation equation. 71,
2.2.2. Integral relations. 75
2.2.3. The addition theorems. 77
2.2. t. Consequences and special cases. 80
2.3 On the computation of the characteristic exponent. 83
2.k. On the eigenvalues for complex h . 85
2.5. Improved estimates of the radii of convergence. 90
2.6. Asymptotic estimates for large h . 96
2.7. On the power series of the eigenvalues. 99
3. Spheroidal Functions. 102
3.1. Integrals with products of spheroidal functions. 102
3.1.1. Integral relations of the first kind. 102
3.1.2. Integral relations of the second kind. 104
3.2. On the eigenvalues for complex y . 106
2
3.3. The spheroidal functions for u = 1, A = 0. 110
i.k. Applications and numerical tables. 113
Appendix. Corrections of errors in MS. 117
Bibliography. 120
|
| any_adam_object | 1 |
| author | Meixner, Josef Schäfke, Friedrich Wilhelm 1922-2010 Wolf, Gerhard |
| author_GND | (DE-588)117720607 |
| author_facet | Meixner, Josef Schäfke, Friedrich Wilhelm 1922-2010 Wolf, Gerhard |
| author_role | aut aut aut |
| author_sort | Meixner, Josef |
| author_variant | j m jm f w s fw fws g w gw |
| building | Verbundindex |
| bvnumber | BV002265859 |
| callnumber-first | Q - Science |
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| dewey-full | 510 515/.54 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics 515 - Analysis |
| dewey-raw | 510 515/.54 |
| dewey-search | 510 515/.54 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:43:03Z |
| institution | BVB |
| isbn | 3540102825 0387102825 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001488963 |
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| physical | VII, 126 S. |
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| publishDate | 1980 |
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| publisher | Springer |
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| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Meixner, Josef Verfasser aut Mathieusche Funktionen und Sphäroidfunktionen Mathieu functions and spheroidal functions and their mathematical foundations further studies Josef Meixner ; Friedrich Wilhelm Schäfke ; Gerhard Wolf Berlin [u.a.] Springer 1980 VII, 126 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 837 Fonctions sphéroïdales Mathieu, Fonctions de Mathieu functions Spheroidal functions Kugelfunktion (DE-588)4033494-6 gnd rswk-swf Sphäroidfunktion (DE-588)4182234-1 gnd rswk-swf Mathieu-Funktion (DE-588)4169113-1 gnd rswk-swf Hill-Differentialgleichung (DE-588)4159882-9 gnd rswk-swf Kugelfunktion (DE-588)4033494-6 s DE-604 Mathieu-Funktion (DE-588)4169113-1 s Hill-Differentialgleichung (DE-588)4159882-9 s Sphäroidfunktion (DE-588)4182234-1 s Schäfke, Friedrich Wilhelm 1922-2010 Verfasser (DE-588)117720607 aut Wolf, Gerhard Verfasser aut Lecture notes in mathematics 837 (DE-604)BV000676446 837 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001488963&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Meixner, Josef Schäfke, Friedrich Wilhelm 1922-2010 Wolf, Gerhard Mathieu functions and spheroidal functions and their mathematical foundations further studies Lecture notes in mathematics Fonctions sphéroïdales Mathieu, Fonctions de Mathieu functions Spheroidal functions Kugelfunktion (DE-588)4033494-6 gnd Sphäroidfunktion (DE-588)4182234-1 gnd Mathieu-Funktion (DE-588)4169113-1 gnd Hill-Differentialgleichung (DE-588)4159882-9 gnd |
| subject_GND | (DE-588)4033494-6 (DE-588)4182234-1 (DE-588)4169113-1 (DE-588)4159882-9 |
| title | Mathieu functions and spheroidal functions and their mathematical foundations further studies |
| title_alt | Mathieusche Funktionen und Sphäroidfunktionen |
| title_auth | Mathieu functions and spheroidal functions and their mathematical foundations further studies |
| title_exact_search | Mathieu functions and spheroidal functions and their mathematical foundations further studies |
| title_full | Mathieu functions and spheroidal functions and their mathematical foundations further studies Josef Meixner ; Friedrich Wilhelm Schäfke ; Gerhard Wolf |
| title_fullStr | Mathieu functions and spheroidal functions and their mathematical foundations further studies Josef Meixner ; Friedrich Wilhelm Schäfke ; Gerhard Wolf |
| title_full_unstemmed | Mathieu functions and spheroidal functions and their mathematical foundations further studies Josef Meixner ; Friedrich Wilhelm Schäfke ; Gerhard Wolf |
| title_short | Mathieu functions and spheroidal functions and their mathematical foundations |
| title_sort | mathieu functions and spheroidal functions and their mathematical foundations further studies |
| title_sub | further studies |
| topic | Fonctions sphéroïdales Mathieu, Fonctions de Mathieu functions Spheroidal functions Kugelfunktion (DE-588)4033494-6 gnd Sphäroidfunktion (DE-588)4182234-1 gnd Mathieu-Funktion (DE-588)4169113-1 gnd Hill-Differentialgleichung (DE-588)4159882-9 gnd |
| topic_facet | Fonctions sphéroïdales Mathieu, Fonctions de Mathieu functions Spheroidal functions Kugelfunktion Sphäroidfunktion Mathieu-Funktion Hill-Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001488963&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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