Electrostatic Problems with a Rational Constraint and Degenerate Lame Equations

Autor(es)

Dimitrov, Dimitar K. ^[1] ; Shapiro, Boris ^[2]

Afiliação do(s) autor(es)

^[1] Univ Estadual Paulista, Dept Matemat Aplicada, IBILCE, BR-15054000 Sao Jose Do Rio Preto, SP - Brazil

^[2] Stockholm Univ, Dept Math, SE-10691 Stockholm - Sweden

• Tipo de documento: Artigo Científico
• Fonte: POTENTIAL ANALYSIS; v. 52, n. 4, p. 645-659, APR 2020.
• Citações Web of Science: 0

Resumo

In 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. (AU)

• Processo FAPESP: 16/09906-0 - Análise harmônica, teoria da aproximação, funções especiais e aplicações
• Beneficiário: Dimitar Kolev Dimitrov
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 17/02061-8 - Teoria de Heine-Stieltjes e eletrostática
• Beneficiário: Dimitar Kolev Dimitrov
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Internacional