Corpus ID: 119158846

Behavior of zeros of $X_{1}$-Jacobi and $X_{1}$-Laguerre exceptional polynomials

@article{Lun2018BehaviorOZ,
  title={Behavior of zeros of \$X\_\{1\}\$-Jacobi and \$X\_\{1\}\$-Laguerre exceptional polynomials},
  author={Yen Chi Lun},
  journal={arXiv: Classical Analysis and ODEs},
  year={2018}
}
  • Y. Lun
  • Published 29 June 2018
  • Mathematics
  • arXiv: Classical Analysis and ODEs
The $X_1$-Jacobi and the $X_1$-Laguerre exceptional orthogonal polynomials have been introduced and studied by G\'omez-Ullate, Kamran and Milson in a series of papers. In this note, we establish some properties, such as interlacing, monotonicity with respect to the parameters and order, about the so-called \textit{regular} and \textit{exceptional} zeros of these two classes of polynomials. 
Asymptotics for recurrence coefficients of X1-Jacobi exceptional polynomials and Christoffel function
  • Á. Horváth
  • Mathematics
  • Integral Transforms and Special Functions
  • 2019
ABSTRACT Computing asymptotics of the recurrence coefficients of -Jacobi polynomials, we investigate the limit of the Christoffel function. We also study the relation between the normalized countingExpand
Asymptotics for Recurrence Coefficients of X1-Jacobi Polynomials and Christoffel Function
Computing asymptotics of the recurrence coefficients of X1-Jacobi polynomials we investigate the limit of Christoffel function. We also study the relation between the normalized counting measureExpand

References

SHOWING 1-10 OF 15 REFERENCES
Monotonicity of zeros of Laguerre polynomials
TLDR
Monotonicity is established with respect to the parameter @a of certain functions involving x"n"k(@a) and sharp upper bounds for the largest zero of L"n^(^@a^)(x) are obtained. Expand
Monotonicity, interlacing and electrostatic interpretation of zeros of exceptional Jacobi polynomials
TLDR
Some properties of the zeros of P n ( α, β ) ( x ) are established, such as interlacing and monotonicity with respect to the parameters α and β, and they turn out to possess an electrostatic interpretation. Expand
Asymptotic and interlacing properties of zeros of exceptional Jacobi and Laguerre polynomials
Abstract In this paper we state and prove some properties of the zeros of exceptional Jacobi and Laguerre polynomials. Generically, the zeros of exceptional polynomials fall into two classes: theExpand
The electrostatic properties of zeros of exceptional Laguerre and Jacobi polynomials and stable interpolation
  • Á. Horváth
  • Computer Science, Mathematics
  • J. Approx. Theory
  • 2015
TLDR
There is a close connection between the electrostatic properties of the zeros and the stability of interpolation on the system of zeros, and an Egervary-Turan type result is deduced. Expand
Zeros of exceptional Hermite polynomials
TLDR
It is shown that the real zeros are distributed as the zeros of usual Hermite polynomials and, after contracting by a factor 2 n , it is proved that they follow the semi-circle law. Expand
Zeros of a family of hypergeometric para-orthogonal polynomials on the unit circle
Para-orthogonal polynomials derived from orthogonal polynomials on the unit circle are known to have all their zeros on the unit circle. In this note we study the zeros of a family of hypergeometricExpand
An extended class of orthogonal polynomials defined by a Sturm-Liouville problem
Abstract We present two infinite sequences of polynomial eigenfunctions of a Sturm–Liouville problem. As opposed to the classical orthogonal polynomial systems, these sequences start with aExpand
A Late Report on Interlacing of Zeros of Polynomials
In this short paper I try to answer questions raised by my teacher Borislav Bojanov which concern interlacing of zeros of real polynomials and consider two specific topics. The first one concerns oneExpand
On the zeros of polynomials
1. This paper deals with the method of D. B erno ulli,1 N. I. Lo batsc h ew sk y2 and N. G raeffe3 devised for the approximative solution of algebraic equations. In the usual form4 the method assertsExpand
An extension of Bochner's problem: Exceptional invariant subspaces
TLDR
The main theorem of the paper provides a characterization of all such differential operators and polynomial sequences based on the classification of codimension one exceptional subspaces under projective transformations. Expand
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