Asymptotics of Pseudo‐Jacobi Polynomials with Varying Parameters. Issue 1 (13th June 2017) - Song, Z.; Wong, R.
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.