# Electrostatic models for zeros of polynomials: Old, new, and some open problems

@article{Marcelln2005ElectrostaticMF, title={Electrostatic models for zeros of polynomials: Old, new, and some open problems}, author={Francisco Marcell{\'a}n and Andrei Mart{\'i}nez-Finkelshtein and Pedro Mart{\'i}nez-Gonz{\'a}lez}, journal={Journal of Computational and Applied Mathematics}, year={2005}, volume={207}, pages={258-272} }

## 48 Citations

### A Unified Approach to Computing the Zeros of Classical Orthogonal Polynomials

- Mathematics
- 2021

The authors present a unified method for calculating the zeros of the classical orthogonal polynomials based upon the electrostatic interpretation and its connection to the energy minimization…

### Approximate Closed-Form Formulas for the Zeros of the Bessel Polynomials

- MathematicsInt. J. Math. Math. Sci.
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These zeros are first computed numerically through an implementation of the electrostatic interpretation formulas and then a fit to the real and imaginary parts as functions of , and it is shown that the resulting complex number is -convergent to for fixed .

### Electrostatic Partners and Zeros of Orthogonal and Multiple Orthogonal Polynomials

- MathematicsConstructive Approximation
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For a given polynomial P with simple zeros, and a given semiclassical weight w, we present a construction that yields a linear second-order differential equation (ODE), and in consequence, an…

### An electrostatic interpretation of the zeros of sieved ultraspherical polynomials

- Mathematics
- 2019

In a companion paper [On semiclassical orthogonal polynomials via polynomial mappings, J. Math. Anal. Appl. (2017)] we proved that the semiclassical class of orthogonal polynomials is stable under…

### Complete solution of the electrostatic equilibrium problem for classical weights

- MathematicsAppl. Math. Comput.
- 2012

### Stable Equilibria for the Roots of the Symmetric Continuous Hahn and Wilson Polynomials

- Mathematics
- 2021

We show that the gradient flows associated with a recently found family of Morse functions converge exponentially to the roots of the symmetric continuous Hahn polynomials. By symmetry reduction the…

### Solvable dynamical systems and isospectral matrices defined in terms of the zeros of orthogonal or otherwise special polynomials.

- Mathematics
- 2018

Several recently discovered properties of multiple families of special polynomials (some orthogonal and some not) that satisfy certain differential, difference or q-difference equations are reviewed.…

### The Diagonal General Case of the Laguerre-Sobolev Type Orthogonal Polynomials

- Mathematics
- 2013

We consider the family of polynomials orthogonal with respect to the Sobolev type inner product corresponding to the diagonal general case of the Laguerre-Sobolev type orthogonal polynomials. We…

### Critical Measures, Quadratic Differentials, and Weak Limits of Zeros of Stieltjes Polynomials

- Mathematics
- 2009

We investigate the asymptotic zero distribution of Heine-Stieltjes polynomials – polynomial solutions of second order differential equations with complex polynomial coefficients. In the case when all…

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