Some applications of Sturm's comparison theorem

Abstract

We consider several classes of orthogonal polynomials as well as the Bessel function where we study the convexity of zeros of these polynomials, satisfying either differential or real difference equations, by applying Sturm's comparison and convexity theorems as well as analogues of these theorems. In addition several results are obtained concerning the distances between consecutive zeros of some of these classes of polynomials. Further research possibilities concerning q-polynomials and polynomials satisfying complex difference equations are discussed.