Some generalizations of p-loxodromic functions

Abstract

The functional equation of the formf(qz) =p(z)f(z), q∈C\{0},|q|<1,z∈C\{0}is considered. For certain fixed elementary functionsp(z),meromorphic solutions of this equation are found. These solutions are somegeneralizations ofp-loxodromic functions and can be represented via theSchottky-Klein prime function as well as classicp-loxodromic functions