Inequalities for Extreme Zeros of Some Classical Orthogonal and q-orthogonal Polynomials

Journal Article

2013

Permanent link to this Item
http://hdl.handle.net/11427/34558
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DriverK_Inequalities_fo_2013.pdf (202.84 KB)
Authors
Driver, K
Jordaan, K
Journal Title

Mathematical Modelling of Natural Phenomena

Link to Journal
https://dx.doi.org/10.1051/mmnp/20138103
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Volume Title
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Publisher
Department
Department of Mathematics and Applied Mathematics
Faculty
Faculty of Science
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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
Article

Reference:

Driver, K. & Jordaan, K. 2013. Inequalities for Extreme Zeros of Some Classical Orthogonal and q-orthogonal Polynomials. Mathematical Modelling of Natural Phenomena. 8(1):48 - 59. http://hdl.handle.net/11427/34558

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