Formulas of the Cauchy and Poisson types for polyanalytic functions are obtained in this work. On the basis of these formulas, the mean-value theorem and the generalized maximum principle are obtained for polyanalytic functions. Estimates for mean values of the associated function of two complex variables on the circles expressed through the mean values of the polyanalytic function itself are obtained. In particular, this implies the estimates for integral norms of analytic components of the polyanalytic function considered.

We discuss conditions for a function bianalytic in the unit disk D = {z : |z| < 1} under which its holomorphic components have angular limits at almost all points ζ ∈ ∂D.