New identities for Legendre associated functions of integral order and degree

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dc.contributor.advisorBrundrit, Geoffen_ZA
dc.contributor.authorSchach, Stephen Ronalden_ZA
dc.date.accessioned2016-01-12T11:19:25Z
dc.date.available2016-01-12T11:19:25Z
dc.date.issued1973en_ZA
dc.description.abstractIn the solution of the boundary value problems of mathematical physics in a separable 3-dimensional coordinate system, the shape of the boundary of the space may be such that the Green's function of the second order differential operator can be expanded as an infinite series of orthogonal functions. In many coordinate systems (such as the spherical, spheroidal and some cyclidal systems) these expansions are given in terms of Legendre associated functions of integral order and degree. Starting with Dougall's identities for Legendre associated functions of non-integral degree, new identities for infinite series of Legendre associated functions of integral degree are derived. Uniform convergence of each new identity is investigated in detail. The direct applicability of these identities is demonstrated by using them to verify theorems satisfied by the Dirichlet Green's function of the infinite half-space and of the interior of the prolate hemispheroid. The results and techniques are then generalized, and a sufficient condition found under which a generalized orthogonal function which satisfies Dougall's identity will also satisfy the new identity. This theorem is applied to the Legendre associated function, the generalized Legendre associated function and to the Jacobi function.en_ZA
dc.identifier.apacitationSchach, S. R. (1973). <i>New identities for Legendre associated functions of integral order and degree</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/16347en_ZA
dc.identifier.chicagocitationSchach, Stephen Ronald. <i>"New identities for Legendre associated functions of integral order and degree."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1973. http://hdl.handle.net/11427/16347en_ZA
dc.identifier.citationSchach, S. 1973. New identities for Legendre associated functions of integral order and degree. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Schach, Stephen Ronald AB - In the solution of the boundary value problems of mathematical physics in a separable 3-dimensional coordinate system, the shape of the boundary of the space may be such that the Green's function of the second order differential operator can be expanded as an infinite series of orthogonal functions. In many coordinate systems (such as the spherical, spheroidal and some cyclidal systems) these expansions are given in terms of Legendre associated functions of integral order and degree. Starting with Dougall's identities for Legendre associated functions of non-integral degree, new identities for infinite series of Legendre associated functions of integral degree are derived. Uniform convergence of each new identity is investigated in detail. The direct applicability of these identities is demonstrated by using them to verify theorems satisfied by the Dirichlet Green's function of the infinite half-space and of the interior of the prolate hemispheroid. The results and techniques are then generalized, and a sufficient condition found under which a generalized orthogonal function which satisfies Dougall's identity will also satisfy the new identity. This theorem is applied to the Legendre associated function, the generalized Legendre associated function and to the Jacobi function. DA - 1973 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 1973 T1 - New identities for Legendre associated functions of integral order and degree TI - New identities for Legendre associated functions of integral order and degree UR - http://hdl.handle.net/11427/16347 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/16347
dc.identifier.vancouvercitationSchach SR. New identities for Legendre associated functions of integral order and degree. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1973 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/16347en_ZA
dc.language.isoengen_ZA
dc.publisher.departmentDepartment of Mathematics and Applied Mathematicsen_ZA
dc.publisher.facultyFaculty of Scienceen_ZA
dc.publisher.institutionUniversity of Cape Town
dc.subject.otherMathematics and Applied Mathematicsen_ZA
dc.titleNew identities for Legendre associated functions of integral order and degreeen_ZA
dc.typeDoctoral Thesis
dc.type.qualificationlevelDoctoral
dc.type.qualificationnamePhDen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
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