A class of hypergeometric polynomials with zeros on the unit circle: Extremal and orthogonal properties and quadrature formulas

Abstract

The class of hypergeometric polynomials F12(−m,b;b+b¯;1−z) with respect to the parameter b=λ+iη, where λ>0, are known to have all their zeros simple and exactly on the unit circle |z|=1. In this note we look at some of the associated extremal and orthogonal properties on the unit circle and on the interval (−1,1). We also give the associated Gaussian type quadrature formulas.