Some holomorphic generalizations of loxodromic functions

  • Dz. V. Lukivska


The functional equation of the form $f(qz) = p(z)f(z), z \in C\setminus \{ 0\} , q \in C\setminus \{ 0\} , | q| < 1$ is considered. For certain fixed elementary functions $p(z)$, holomorphic solutions of this equation are found. These solutions are some generalizations of loxodromic functions. Some of solutions are represented via the Schottky – Klein prime function.
How to Cite
LukivskaD. V. “Some Holomorphic Generalizations of Loxodromic Functions”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 69, no. 9, Sept. 2017, pp. 1284-8,
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