Asymptotics of Pseudo‐Jacobi Polynomials with Varying Parameters. Issue 1 (13th June 2017)

• Record Type: Journal Article
• Authors: Song, Z.; Wong, R.
• Is Part Of: Studies in applied mathematics. Volume 139:Issue 1(2017)
• Page Start: 179
• Page End: 217
• Publication Date: 2017-06-13
• Subjects: Mathematics -- Periodicals; Mathématiques -- Périodiques; Mathématique; Mathématique appliquée; Ressource Internet (Descripteur de forme); Périodique électronique (Descripteur de forme); 519
• DOI: 10.1111/sapm.12177
• Languages: English
• ISSNs: 0022-2526

Abstract

Abstract : In this paper, we study the asymptotic behavior of the Pseudo‐Jacobi polynomials P n ( z ; a, b ) as n → ∞ for z in the whole complex plane. These polynomials are also known as the Romanovski–Routh polynomials. They occur in quantum mechanics, quark physics, and random matrix theory. When the parameter a is fixed or a > − n, there is no real‐line orthogonality. Here, we consider the case when the parameters a and b depend on n ; more precisely, we assume a = − ( A n + A 0 ), A > 1 and b = B n + B 0, where A, B, A 0, B 0 are real constants. Our main tool is the asymptotic method developed for differential equations with a large parameter.