External Ellipsoidal Harmonics for the Dunkl-Laplacian
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...
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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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The sphere, because of its high symmetry, is what might be called a perfect shape. Unfortunately nature is imperfect and many apparently spherical bodies are better represented by an ellipsoid. Consequently in calculations about gravitational potential, for example, spherical harmonics have to be replaced by the much more complex ellipsoidal harmonics. Their theory, which was originated in the ...
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ژورنال
عنوان ژورنال: Symmetry, Integrability and Geometry: Methods and Applications
سال: 2008
ISSN: 1815-0659
DOI: 10.3842/sigma.2008.091