*Math. Model. Nat. Phenom.*Vol. 8, No. 1, 2013, pp. 48-59

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

^{1} Department of Mathematics and Applied
Mathematics, University of
Cape Town
7701,
RSA ^{2} Department of Mathematics and Applied
Mathematics, University of Pretoria, Pretoria, 0002, RSA

^{∗} Corresponding author. E-mail: kathy.driver@uct.ac.za

Let {*p _{n}*}

^{∞}

_{n=0}be a sequence of orthogonal polynomials. We briefly review properties of

*p*

_{n}that have been used to derive upper and lower bounds for the largest and smallest zero of

*p*

_{n}

*.*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.

Mathematics Subject Classification: 33C45 / 42C05

Key words: Bounds for extreme zeros of orthogonal and q-orthogonal polynomials / common zeros of orthogonal polynomials / monotonicity / convexity / interlacing of zeros / separation of zeros / inequalities for zeros

*© EDP Sciences, 2013*