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separation of zeros

Mathematical Modelling of Natural Phenomena (1)

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Inequalities for Extreme Zeros of Some Classical Orthogonal andq-orthogonal Polynomials
K. Driver, K. Jordaan
Journal:

Mathematical Modelling of Natural Phenomena / Volume 8 / Issue 1 / 2013

Published online by Cambridge University Press:

28 January 2013, pp. 48-59

Print publication:

2013
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Let {pn}∞n=0 be a sequence of orthogonal polynomials. We brieflyreview properties of pn that have been usedto derive upper and lower bounds for the largest and smallest zero ofpn. Bounds for theextreme zeros of Laguerre, Jacobi and Gegenbauer polynomials that have been obtained usingdifferent approaches are numerically compared and new bounds for extreme zeros ofq-Laguerre and little q-Jacobi polynomials are proved.