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- W2963314660 abstract "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 Lamé 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 Lamé 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." @default.
- W2963314660 created "2019-07-30" @default.
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- W2963314660 date "2018-12-18" @default.
- W2963314660 modified "2023-10-18" @default.
- W2963314660 title "Electrostatic Problems with a Rational Constraint and Degenerate Lamé Equations" @default.
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- W2963314660 doi "https://doi.org/10.1007/s11118-018-9754-y" @default.
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