Numerical problems in the computation of ellipsoidal harmonics
نویسندگان
چکیده
منابع مشابه
External Ellipsoidal Harmonics for the Dunkl–Laplacian⋆
Following the book [9] by Dunkl and Xu and the paper [23] by Xu we will assume that αj ≥ 0 for each j = 0, 1, . . . , k although one would expect that the range of validity can be extended analytically to the domain αj > −12 for each j. We will also exclude the case k = 1, α0 = α1 = 0 because we want the constant μ defined below in (1.5) to be positive. The parity vector p = (p0, p1, . . . , pk...
متن کاملGeneralized Ellipsoidal and Sphero-Conal Harmonics
Classical ellipsoidal and sphero-conal harmonics are polynomial solutions of the Laplace equation that can be expressed in terms of Lamé polynomials. Generalized ellipsoidal and sphero-conal harmonics are polynomial solutions of the more general Dunkl equation that can be expressed in terms of Stieltjes polynomials. Niven’s formula connecting ellipsoidal and sphero-conal harmonics is generalize...
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We present two open-source (BSD) implementations of ellipsoidal harmonic expansions for solving problems of potential theory using separation of variables. Ellipsoidal harmonics are used surprisingly infrequently, considering their substantial value for problems ranging in scale from molecules to the entire solar system. In this paper, we suggest two possible reasons for the paucity relative to...
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Jaydeep P. Bardhan and Matthew G. Knepley Dept. of Molecular Biophysics and Physiology, Rush University Medical Center, Chicago IL 60612 Computation Institute, The University of Chicago, Chicago IL 60637 Abstract We present two open-source (BSD) implementations of ellipsoidal harmonic expansions for solving problems of potential theory using separation of variables. Ellipsoidal harmonics are us...
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ژورنال
عنوان ژورنال: Journal of Geodesy
سال: 1995
ISSN: 0949-7714,1432-1394
DOI: 10.1007/bf00863423