Complementary Romanovski-Routh polynomials and their zeros - Silva Ribeiro, L. L.; Sri Ranga, A.; Chi Lun, Yen (Trends in Computational and Applied Mathematics, 2025)
The efficacy of numerical methods like integral estimates via Gaussian quadrature formulas depends on the localization of the zeros of the associated family of orthogonal polynomials. Following the renewed interest in quadrature formulas on the unit circle and RII type polynomials, in this work we present properties satisfied by the zeros of the complementary Romanovski-Routh polynomials. Our results include extreme bounds, convexity, density, and the connection of such zeros with the zeros of classical orthogonal polynomials via asymptotic formulas.