| Full text | |
| Author(s): |
Total Authors: 2
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| Affiliation: | [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
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | POTENTIAL ANALYSIS; v. 52, n. 4, p. 645-659, APR 2020. |
| Web of Science Citations: | 0 |
| 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 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) | |
| FAPESP's process: | 16/09906-0 - Harmonic analysis, approximation theory and applications |
| Grantee: | Dimitar Kolev Dimitrov |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 17/02061-8 - Heine-Stieltjes theory and electrostatics |
| Grantee: | Dimitar Kolev Dimitrov |
| Support Opportunities: | Research Grants - Visiting Researcher Grant - International |