Our interest lies in describing the zero behaviour of Gauss hypergeometric polynomials F (−n, b; c; z) where b and c are arbitrary parameters. In general, this problem has not been solved and even when b and c are both real, the only cases that have been fully analyzed impose additional restrictions on b and c. We review recent results that have been proved for the zeros of several classes of h...

In a celebrated paper, Borwein, Erdélyi, Ferguson and Lockhart constructed cosine polynomials of the form f A ( x ) = ∑ ∈ cos , with ⊆ N | n as few 5 / 6 + o 1 zeros in [ 0 2 π ] thereby disproving an old conjecture Littlewood. Here we give sharp analysis their constructions and, result, prove that there exist examples C log 3 zeros.

We prove several results about zeros of paraorthogonal polynomials using the theory of rank one perturbations of unitary operators. In particular, we obtain new details on the interlacing of zeros for successive POPUC. © 2006 Elsevier Inc. All rights reserved.

The main object of this paper is to consider the asymptotic distribution of the zeros of certain classes of the Clausenian hypergeometric 3F2 functions and polynomials. Some classical analytic methods and techniques are used here to analyze the behavior of the zeros of the Clausenian hypergeometric polynomials: 3F2(−n, τn+ a, b; τn+ c,−n+ d; z), where n is a nonnegative integer. Some families o...

A fourth order fixed point method to compute the zeros of solutions of second order homogeneous linear ODEs is obtained from the approximate integration of the Riccati equation associated with the ODE. The method requires the evaluation of the logarithmic derivative of the function and also uses the coefficients of the ODE. An algorithm to compute with certainty all the zeros in an interval is ...