On complex harmonic typically-real functions with a pole at the point zero

Abstract

Several mathematicians examined classes of meromorphic typically-real functions with a simple pole at the point zero. This article includes results concern class Q' H of complex harmonic typically-real functions with a pole at the point zero. There are determined the relationships between this class and the class Q' r of meromorphic typically-real funtions with a pole at the origin, which was investigated by S. A. Gelfer [4]. We present also coefficient estimates for functions of a subclass of the class Q' H and properties of the Hadamard product with fuctions of the class Q' H.