Bounds for extreme zeros of Meixner–Pollaczek polynomials
Year: 2024
Type: article
Abstract: In this paper we consider connection formulae for orthogonal polynomials in the context of Christoffel transformations for the case where a weight function, not necessarily even, is multiplied by an even function c 2 k ( x ) , k ∈ N 0 , to determine new lower bounds for the largest zero and upper bounds for the smallest zero of a Meixner–Pollaczek polynomial. When p n is orthogonal with respect to a weight w ( x ) and g n − m is orthogonal with respect to the weight c 2 k ( x ) w ( x ) , we show that k ∈ { 0 , 1 , … , m } is a necessary and sufficient condition for existence of a connection formula involving a polynomial G m − 1 of degree ( m − 1 ) , such that the ( n − 1 ) zeros of G m − 1 g n − m and the n zeros of p n interlace. We analyse the new inner bounds for the extreme zeros of Meixner–Pollaczek polynomials to determine which bounds are the sharpest. We also briefly discuss bounds for the zeros of Pseudo-Jacobi polynomials.
Source: Journal of Approximation Theory
Authors: A.S. Jooste, K. Jordaan
Institutions: University of Pretoria, University of South Africa
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,830
OpenAlex ID: W4405662840