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Generalized Legendre series and the fundamental solution of the Laplacian on the n-sphere

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Summary

Classical representations of the Legendre polynomials in terms of generating functions are nonconvergent in the usual sense for extreme values of the generating parameter. A generalized type of convergence is explored and, in conjunction with the theory of Fourier series and spherical harmonics, it is applied to the computation of the fundamental solution of the Laplace-Beltrami operator on the n-sphere.

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Martinez-Morales, J. Generalized Legendre series and the fundamental solution of the Laplacian on the n-sphere. Anal Math 31, 131–150 (2005). https://doi.org/10.1007/s10476-005-0009-y

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  • DOI: https://doi.org/10.1007/s10476-005-0009-y

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