Spherical harmonics in a non-polar co-ordinate system and application to Fourier series in 2-sphere

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A new non-polar spherical co-ordinate system for the three-dimensional space is introduced. The co-ordinate system is composed of six local co-ordinate systems mapped from six faces of a cube on to the 2-sphere. Weakly orthogonal and orthogonal spherical harmonics are constructed in this coordinate system. The spherical harmonics are easily computable functions consisting of polynomials and square root of polynomials. Examples of finite Fourier series computations are given in terms of the new spherical harmonics to demonstrate their immediate applicability.

Original languageEnglish
Pages (from-to)1843-1854
Number of pages12
JournalMathematical Methods in the Applied Sciences
Issue number14
Publication statusPublished - Sep 25 2007



  • Curvilinear co-ordinate systems
  • Fourier series on 2-sphere
  • Laplace-Beltrami operator
  • Spherical harmonics

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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