## 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.

Author: Frank Bauer urn:nbn:de:hbz:386-kluedo-14018 Schriften zur Funktionalanalysis und Geomathematik (24) Preprint English 2005 2005 Technische Universität Kaiserslautern 2005/12/02 Derivatives; Spherical Harmonics Kugelflächenfunktion ; Richtungsableitung Fachbereich Mathematik 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik 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 Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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