Easy Differentiation and Integration of Homogeneous Harmonic Polynomials
- We will give explicit differentiation and integration rules for homogeneous harmonic polynomial polynomials and spherical harmonics in IR^3 with respect to the following differential operators: partial_1, partial_2, partial_3, x_3 partial_2 - x_2 partial_3, x_3 partial_1 - x_1 partial_3, x_2 partial_1 - x_1 partial_2 and x_1 partial_1 + x_2 partial_2 + x_3 partial_3. A numerical application to the problem of determining the geopotential field will be shown.
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| Author: | Frank Bauer |
|---|---|
| URN: | urn:nbn:de:hbz:386-kluedo-14018 |
| Series (Serial Number): | Schriften zur Funktionalanalysis und Geomathematik (24) |
| Document Type: | Preprint |
| Language of publication: | English |
| Year of Completion: | 2005 |
| Year of first Publication: | 2005 |
| Publishing Institution: | Technische Universität Kaiserslautern |
| Date of the Publication (Server): | 2005/12/02 |
| Tag: | Derivatives; Spherical Harmonics |
| GND Keyword: | Kugelflächenfunktion; Richtungsableitung |
| Faculties / Organisational entities: | Kaiserslautern - Fachbereich Mathematik |
| DDC-Cassification: | 5 Naturwissenschaften und Mathematik / 510 Mathematik |
| MSC-Classification (mathematics): | 33-XX SPECIAL FUNCTIONS (33-XX DEALS WITH THE PROPERTIES OF FUNCTIONS AS FUNCTIONS) (For orthogonal functions, see 42Cxx; for aspects of combinatorics see 05Axx; for number-theoretic aspects see 11-XX; for representation theory see 22Exx) / 33Cxx Hypergeometric functions / 33C55 Spherical harmonics |
| Licence (German): |  Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011 |