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Exact computation of spherical harmonics

Exakte Berechnung von Kugelfunktionen

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Abstract

Essential results of the theory of spherical harmonics are recapitulated by intrinsic properties of the space of homogeneous harmonic polynomials of degreen and dimensionq.

The theoretical considerations are used to describe an alternate method to the conventional procedure of constructing spherical harmonics by recursion. The numerical efficiency is explained, examples are given for the threedimensional case.

Zusammenfassung

Wesentliche Eigenschaften der Theorie der Kugelfunktionen werden rekapituliert durch innere Eigenschaften des Raumes der homogenen harmonischen Polynome vom Graden inq Dimensionen.

Die theoretischen Betrachtungen werden benutzt, um eine Alternative zur konventionellen Methode der Konstruktion von Kugelfunktionen durch Rekursion zu beschreiben. Die numerische Effektivität wird erläutert, Beispiele werden angegeben für den dreidimensionalen Fall.

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References

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Authors and Affiliations

  1. Institut für Reine und Angewandte Mathematik, RWTH Aachen, Templergraben 55, D-5100, Aachen, Federal Republic of Germany

    W. Freeden

  2. Rechenzentrum, RWTH Aachen, Seffenter Weg 23, D-5100, Aachen, Federal Republic of Germany

    R. Reuter

Authors
  1. W. Freeden
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  2. R. Reuter
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Freeden, W., Reuter, R. Exact computation of spherical harmonics. Computing 32, 365–378 (1984). https://doi.org/10.1007/BF02243779

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  • DOI: https://doi.org/10.1007/BF02243779

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