Inequalities for extreme zeros of some classical orthogonal and q-orthogonal polynomials
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Date
Authors
Driver, Kathy (Cathryn Helena Stanford)
Jordaan, Kerstin Heidrun
Journal Title
Journal ISSN
Volume Title
Publisher
Cambridge University Press
Abstract
Let {pn}1
n=0 be a sequence of orthogonal polynomials. We briefly review properties
of pn that have been used to derive upper and lower bounds for the largest and smallest zero
of pn. Bounds for the extreme zeros of Laguerre, Jacobi and Gegenbauer polynomials that have
been obtained using different approaches are numerically compared and new bounds for extreme
zeros of q-Laguerre and little q-Jacobi polynomials are proved.
Description
Keywords
Bounds for extreme zeros of orthogonal and q-orthogonal polyno-mials, Common zeros of orthogonal polynomials, Monotonicity, Convexity, Interlacing of zeros, Separation of zeros, Inequalities for zeros
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Citation
Driver, K & Jordaan, K 2013, 'Inequalities for extreme zeros of some classical orthogonal and q-orthogonal polynomials', Mathematical Modelling of Natural Phenomena, vol. 8, no. 1, pp. 48-59.