Positivity of Tur\'an determinants for orthogonal polynomials
Ryszard Szwarc

TL;DR
This paper establishes general criteria for when orthogonal polynomials satisfy Turán's inequality, extending known results to new polynomial families like the q-ultraspherical polynomials.
Contribution
It provides new theoretical criteria for Turán's inequality in orthogonal polynomials, including novel results for q-ultraspherical polynomials.
Findings
Criteria for Turán's inequality in orthogonal polynomials
Extension of known results to new polynomial families
Application to q-ultraspherical polynomials
Abstract
The orthogonal polynomials satisfy Tur\'an's inequality if for and for all in the interval of orthogonality. We give general criteria for orthogonal polynomials to satisfy Tur\'an's inequality. This yields the known results for classical orthogonal polynomials as well as new results, for example, for the --ultraspherical polynomials.
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Taxonomy
TopicsStatistical and numerical algorithms · Mathematical functions and polynomials · Iterative Methods for Nonlinear Equations
