Design of a Mathematica package to develop the product of some spherical functions as linear combinations of themselves
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Altres documents de l'autoria: Forner Gumbau, Manuel; Barreda Rochera, Miguel; López Ortí, José Antonio
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https://doi.org/10.1002/cmm4.1052 |
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Títol
Design of a Mathematica package to develop the product of some spherical functions as linear combinations of themselvesData de publicació
2019-09Editor
WileyISSN
2577-7408Cita bibliogràfica
FORNER GUMBAU, Manuel; BARREDA ROCHERA, Miguel; LÓPEZ ORTÍ, José Antonio. Design of a Mathematica package to develop the product of some spherical functions as linear combinations of themselves. Computational and Mathematical Methods, 2019, vol. 1, no 5, p. e1052.Tipus de document
info:eu-repo/semantics/articleVersió de l'editorial
https://onlinelibrary.wiley.com/doi/full/10.1002/cmm4.1052Versió
info:eu-repo/semantics/publishedVersionParaules clau / Matèries
Resum
Results obtained when solving problems about atomic physics and about the potential theory show an almost spherical symmetry. These solutions can only be expressed in an exact form on a few occasions, so turning to ... [+]
Results obtained when solving problems about atomic physics and about the potential theory show an almost spherical symmetry. These solutions can only be expressed in an exact form on a few occasions, so turning to approximations of these solutions through spherical functions becomes necessary. To achieve these approximations, it is necessary to obtain the product of two or more spherical functions as a linear combination of them. In this work, some formulas expressing the products of Legendre polynomials, associated Legendre functions and spherical harmonics, as linear combination of themselves, are presented. To do so, the bases for the algebraic manipulations of the previous products are first established. Subsequently, analytical developments with exact coefficients of those products are obtained. A software package has also been programmed with Mathematica program to obtain, in a simple and practical way, the aforementioned developments. [-]
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Computational and Mathematical Methods, 2019, vol. 1, no 5Proyecto de investigación
Jaume I University of Castellón: 16I358.01/1Drets d'accés
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