Abstract
The preceding chapter has described the general properties of the spaces Y n (q), but there is a need to fill the general frame with concrete and explicit data. We have seen that the Legendre polynomials contain all that is necessary to determine an orthonormal system of spherical harmonics. This chapter is therefore devoted to the Pn(q; ·) and their many relations and possibilities. This part contains only a selection of identities and special results. An explicit orthogonal basis of yn (q) was found by Laplace for q = 3. His discovery can be easily extended to higher dimensions. We add a description of the isotropically invariant associated spaces.
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© 1998 Springer Science+Business Media New York
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Müller, C. (1998). The Specific Theories. In: Analysis of Spherical Symmetries in Euclidean Spaces. Applied Mathematical Sciences, vol 129. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0581-4_3
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DOI: https://doi.org/10.1007/978-1-4612-0581-4_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6827-7
Online ISBN: 978-1-4612-0581-4
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