2017
Том 69
№ 9

All Issues

On the Regular Variation of Main Characteristics of an Entire Function

Filevych P. V., Sheremeta M. M.

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Abstract

We establish a necessary and sufficient condition for the coefficients a n of an entire function \(f(z) = \sum {_{n = 0}^\infty } {\text{ }}a_n z^n \) under which its central index and the logarithms of the maximum of the modulus and the maximum term are regularly varying functions. We construct an entire function the logarithm of the maximum of whose modulus is a regularly varying function, whereas the Nevanlinna characteristic function is not a regularly varying function.

English version (Springer): Ukrainian Mathematical Journal 55 (2003), no. 6, pp 1012-1024.

Citation Example: Filevych P. V., Sheremeta M. M. On the Regular Variation of Main Characteristics of an Entire Function // Ukr. Mat. Zh. - 2003. - 55, № 6. - pp. 840-849.

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