Hadamard Compositions of Gelfond–Leont’ev Derivatives

Author:

Sheremeta MyroslavORCID

Abstract

For analytic functions fj(z)=∑n=0∞an,jzn, 1≤j≤p, the notion of a Hadamard composition (f1∗…∗fp)m=∑n=0∞∑k1+⋯+kp=mck1…kpan,1k1·…·an,pkpzn of genus m is introduced. The relationship between the growth of the Gelfond–Leont’ev derivative of the Hadamard composition of functions fj and the growth Hadamard composition of Gelfond–Leont’ev derivatives of these functions is studied. We found conditions under which these derivatives and the composition have the same order and a lower order. For the maximal terms of the power expansion of these derivatives, I describe behavior of their ratios.

Publisher

MDPI AG

Subject

Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis

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