Abstract
In a previous paper the authors have developed a method for exact computation of basis systems of homogeneous harmonic polynomials of degree n = 0,1,... in IRq using exclusively integer operations. The critical point in that approach is that all members of the basis system of degree n are involved in the computations if one is interested in finding an orthonormalized system of spherical harmonics of degree n on the unit sphere Ω q in IRq. In this paper it is shown that the amount of computational work can be reduced drastically if the orthonormalization process is based on the fact that any homogeneous harmonic polynomial of degree n in IRq can be recovered from any two homogeneous harmonic polynomials inR q -1 of degree n and n - 1.
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References
Freeden, W.; Reuter, R.: Exact Computation of Spherical Harmonics. Computing, (32) pp 365–378, 1984.
Muller, Cl.: Spherical Harmonics. Lecture Notes in Mathematics 17, Springer, Berlin, Heidelberg, New York, 1966.
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© 1990 Chapman and Hall
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Freeden, W., Reuter, R. (1990). An efficient algofithm for the generation of homogeneous harmonic polynomials. In: Mason, J.C., Cox, M.G. (eds) Scientific Software Systems. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0841-3_12
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DOI: https://doi.org/10.1007/978-94-009-0841-3_12
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-6865-9
Online ISBN: 978-94-009-0841-3
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