On the rate of approximation in the unit disc of -functions by logarithmic derivatives of polynomials with zeros on the boundary

We study uniform approximation in the open unit disc by logarithmic derivatives of -polynomials, that is, polynomials whose zeros lie on the unit circle . We find bounds for the rate of approximation for functions in Hardy class and certain subclasses. We prove bounds for the rate of uniform approximation (either in or its closure) by -sums with parameters .