Open Access
VOL. 5 | 2004 The Zeros of Polynomials Orthogonal with Respect to $q$-Integral on Several Intervals in the Complex Plane
Predrag M. Rajkovic, Miomir S. Stankovic, Sladjana D. Marinkovic

Editor(s) Ivaïlo M. Mladenov, Allen C. Hirshfeld

Geom. Integrability & Quantization, 2004: 178-188 (2004) DOI: 10.7546/giq-5-2004-178-188


We construct the sequence of orthogonal polynomials with respect to an inner product defined in the sense of $q$-integration over several intervals in the complex plane. For such introduced polynomials we prove that all zeros lie in the smallest convex hull over the intervals in the complex plane. The results are stated precisely in some special cases, as some symmetric cases of equal lengths, angles and weights.


Published: 1 January 2004
First available in Project Euclid: 12 June 2015

zbMATH: 1061.33016
MathSciNet: MR2082303

Digital Object Identifier: 10.7546/giq-5-2004-178-188

Rights: Copyright © 2004 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences


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