Zeros of the Exceptional Laguerre and Jacobi Polynomials. (11th September 2012)

• Record Type: Journal Article
• Authors: Ho, Choon-Lin; Sasaki, Ryu
• Other Names: Goldin G. Academic Editor.; Schiappa R. Academic Editor.
• Is Part Of: ISRN mathematical physics. Volume 2012(2012)
• Publication Date: 2012-09-11
• Subjects: Mathematical physics -- Periodicals; Mathematical physics; Electronic journals; Periodicals; 530.15
• DOI: 10.5402/2012/920475
• Languages: English
• ISSNs: 2090-4673

Abstract

Abstract : An interesting discovery in the last two years in the field of mathematical physics has been the exceptional X ℓ Laguerre and Jacobi polynomials. Unlike the well-known classical orthogonal polynomials which start with constant terms, these new polynomials have the lowest degree ℓ = 1, 2, …, and yet they form complete sets with respect to some positive-definite measure. In this paper, we study one important aspect of these new polynomials, namely, the behaviors of their zeros as some parameters of the Hamiltonians change. Most results are of heuristic character derived by numerical analysis.