Electrostatic Problems with a Rational Constraint and Degenerate Lame Equations

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dc.contributor.authorDimitrov, Dimitar K. [UNESP]
dc.contributor.authorShapiro, Boris
dc.contributor.institutionUniversidade Estadual Paulista (Unesp)
dc.contributor.institutionStockholm Univ
dc.date.accessioned2020-12-10T19:57:18Z
dc.date.available2020-12-10T19:57:18Z
dc.date.issued2020-04-01
dc.description.abstractIn this note we extend the classical relation between the equilibrium configurations of unit movable point charges in a plane electrostatic field created by these charges together with some fixed point charges and the polynomial solutions of a corresponding Lame differential equation. Namely, we find similar relation between the equilibrium configurations of unit movable charges subject to a certain type of rational or polynomial constraint and polynomial solutions of a corresponding degenerate Lame equation, see details below. In particular, the standard linear differential equations satisfied by the classical Hermite and Laguerre polynomials belong to this class. Besides these two classical cases, we present a number of other examples including some relativistic orthogonal polynomials and linear differential equations satisfied by those.en
dc.description.affiliationUniv Estadual Paulista, Dept Matemat Aplicada, IBILCE, BR-15054000 Sao Jose Do Rio Preto, SP, Brazil
dc.description.affiliationStockholm Univ, Dept Math, SE-10691 Stockholm, Sweden
dc.description.affiliationUnespUniv Estadual Paulista, Dept Matemat Aplicada, IBILCE, BR-15054000 Sao Jose Do Rio Preto, SP, Brazil
dc.description.sponsorshipFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
dc.description.sponsorshipConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
dc.description.sponsorshipIdFAPESP: 2016/09906-0
dc.description.sponsorshipIdFAPESP: 2017/02061-8
dc.description.sponsorshipIdCNPq: 306136/2017-1
dc.format.extent645-659
dc.identifierhttp://dx.doi.org/10.1007/s11118-018-9754-y
dc.identifier.citationPotential Analysis. Dordrecht: Springer, v. 52, n. 4, p. 645-659, 2020.
dc.identifier.doi10.1007/s11118-018-9754-y
dc.identifier.issn0926-2601
dc.identifier.urihttp://hdl.handle.net/11449/196824
dc.identifier.wosWOS:000528380600005
dc.language.isoeng
dc.publisherSpringer
dc.relation.ispartofPotential Analysis
dc.sourceWeb of Science
dc.subjectElectrostatic equilibrium
dc.subjectLame differential equation
dc.titleElectrostatic Problems with a Rational Constraint and Degenerate Lame Equationsen
dc.typeArtigo
dcterms.licensehttp://www.springer.com/open+access/authors+rights?SGWID=0-176704-12-683201-0
dcterms.rightsHolderSpringer
unesp.author.orcid0000-0002-3078-2336[1]
unesp.author.orcid0000-0002-8438-3971[2]

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Artigos - Matemática Aplicada - IBILCE