Zeros of polynomials orthogonal with respect to a signed weight
M. Benabdallah, M. J. Atia, R. S. Costas-Santos

TL;DR
This paper studies the zeros of a specific polynomial sequence orthogonal with respect to a signed weight, providing new recurrence coefficients, analyzing zero interlacing properties, and establishing inequalities among the largest zeros.
Contribution
It introduces a novel method for deriving recurrence coefficients and analyzes zero distribution properties for polynomials orthogonal with a signed weight.
Findings
Recurrence coefficients are explicitly obtained using a new method.
Interlacing property of zeros does not hold properly for these polynomials.
Largest zeros satisfy specific inequalities depending on parameters.
Abstract
In this paper we consider the polynomial sequence that is orthogonal on with respect to the weight function ; we obtain the coefficients of the tree-term recurrence relation (TTRR) by using a different method from the one derived in \cite{kn:atia1}; we prove that the interlacing property does not hold properly for ; and we also prove that, if is the largest zero of , .
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