Abstract
The orthogonal polynomials p n satisfy Turán’s inequality if pn 2(x)-pn-1(x)pn+1(x) ≥ 0 for ≥ 1 and for all x in the interval of orthogonality. We give general criteria for orthogonal polynomials to satisfy Turán’s inequality. This yields the known results for classical orthogonal polynomials as well as new results, for example, for the q-ultraspherical polynomials.
This work has been partially supported by KBN (Poland) under grant 2 P03A 030 09.
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Szwarc, R. (1998). Positivity of Turán Determinants for Orthogonal Polynomials. In: Ross, K.A., Singh, A.I., Anderson, J.M., Sunder, V.S., Litvinov, G.L., Wildberger, N.J. (eds) Harmonic Analysis and Hypergroups. Trends in Mathematics. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-4348-5_11
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DOI: https://doi.org/10.1007/978-0-8176-4348-5_11
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