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

The class of hypergeometric polynomials F 1 2 ( − m , b ; b + b ¯ ; 1 − z ) with respect to the parameter b = λ + i η , 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.