Abstract
We study the asymptotic behavior of the zeros of polynomial solutions of a class of generalized Lamé differential equations, when their coefficients satisfy certain asymptotic conditions. The limit distribution is described by an equilibrium measure in the presence of an external field, generated by charges at the singular points of the equation. Moreover, a case of non-positive charges is considered, which leads to an equilibrium with a non-convex external field.
| Original language | English |
|---|---|
| Pages (from-to) | 131-151 |
| Number of pages | 21 |
| Journal | Journal of Approximation Theory |
| Volume | 118 |
| Issue number | 1 |
| DOIs | |
| State | Published - 1 Sep 2002 |
| Externally published | Yes |
Keywords
- Electrostatics
- Equilibrium distribution
- Generalized lamé differential equation
- Heine-Stieltjes polynomials
- Logarithmic potential
- Van Vleck polynomials
- Zero asymptotics
ASJC Scopus subject areas
- Analysis
- Numerical Analysis
- General Mathematics
- Applied Mathematics