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dc.contributor.authorE. O. Jobunga
dc.contributor.authorO. S. Okeyo
dc.date.accessioned2022-03-29T12:46:09Z
dc.date.available2022-03-29T12:46:09Z
dc.date.issued2020
dc.identifier.urihttps://ir.tum.ac.ke/handle/123456789/17454
dc.description.abstractLegendre polynomials form the basis for multipole expansion of spatially varying functions. The technique allows for decomposition of the function into two separate parts with one depending on the radial coordinates only and the other depending on the angular variables. In this work, the angular function cosk θ is expanded in the Legendre polynomial basis and the algorithm for determining the corresponding coefcients of the Legendre polynomials is generated. This expansion together with the algorithm can be generalized to any case in which a dot product of any two vectors appears. Two alternative multipole expansions for the electron–electron Coulomb repulsion term are obtained. It is shown that the conventional multipole expansion of the Coulomb repulsion term is a special case for one of the expansions generated in this work.en_US
dc.language.isoenen_US
dc.publisherScientific reports - nature researchen_US
dc.relation.ispartofseries;2020) 10:20126
dc.subjectLegendre polynomialsen_US
dc.subjectmultipoleen_US
dc.subjectelectron-electron repulsionen_US
dc.titleMultipole expansion of integral powers of cosine thetaen_US
dc.typeArticleen_US


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