Exceptional Legendre Polynomials and Confluent Darboux Transformations

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2021
• Main Authors: García-Ferrero, María Ángeles, Gómez-Ullate, David, Milson, Robert
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2021
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/211172
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Exceptional Legendre Polynomials and Confluent Darboux Transformations. María Ángeles García-Ferrero, David Gómez-Ullate and Robert Milson. SIGMA 17 (2021), 016, 19 pages

Exceptional orthogonal polynomials are families of orthogonal polynomials that arise as solutions of Sturm-Liouville eigenvalue problems. They generalize the classical families of Hermite, Laguerre, and Jacobi polynomials by allowing for polynomial sequences that miss a finite number of ''...