Exceptional Laguerre polynomials
arXiv:1708.03106 · doi:10.1111/sapm.12204
Abstract
The aim of this paper is to present the construction of exceptional Laguerre polynomials in a systematic way, and to provide new asymptotic results on the location of the zeros. To describe the exceptional Laguerre polynomials we associate them with two partitions. We find that the use of partitions is an elegant way to express these polynomials and we restate some of their known properties in terms of partitions. We discuss the asymptotic behavior of the regular zeros and the exceptional zeros of exceptional Laguerre polynomials as the degree tends to infinity.
To appear in Studies in Applied Mathematics
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Cited by in corpus (10)
- Exceptional Jacobi polynomials
- Coefficients of Wronskian Hermite polynomials
- Rational Solutions of the Fifth Painlevé Equation. Generalised Laguerre Polynomials
- Wronskian Appell Polynomials and Symmetric Functions
- Recurrence Relations for Wronskian Hermite Polynomials
- General solution of the exceptional Hermite differential equation and its minimal surface representation
- Discrete orthogonality relations for multi-indexed Laguerre and Jacobi polynomials
- Lectures on exceptional orthogonal polynomials and rational solutions to Painlevé equations
- Recurrence relations for Wronskian Laguerre polynomials
- Determinantal Formulas for Exceptional Orthogonal Polynomials