Spherical Harmonics in \({\mathbb{R}}^{q}\)

  • Willi Freeden
  • Martin Gutting
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)


The theory of scalar spherical harmonics of  Chap. 4can be generalized to spheres in the q-dimensional space, i.e., from \({\mathbb{S}}^{2} \subset {\mathbb{R}}^{3}\) to \({\mathbb{S}}^{q-1} \subset {\mathbb{R}}^{q}\). Obviously, this leads to a more extensive notation and makes some formulas a bit unwieldy. However, many proofs and the whole line of thought of the three-dimensional case carry over to the general setting such that we can skip some details that are analogous.


Unit Sphere Spherical Harmonic Legendre Polynomial Sphere Function Orthonormal System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer Basel 2013

Authors and Affiliations

  • Willi Freeden
    • 1
  • Martin Gutting
    • 1
  1. 1.Geomathematics GroupUniversity of KaiserslauternKaiserslauternGermany

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