Electrostatic Problems with a Rational Constraint and Degenerate Lame Equations
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Data
2020-04-01
Autores
Dimitrov, Dimitar K. [UNESP]
Shapiro, Boris
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Springer
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.
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Electrostatic equilibrium, Lame differential equation
Como citar
Potential Analysis. Dordrecht: Springer, v. 52, n. 4, p. 645-659, 2020.