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MATHEMATICS
On the type of the meromorphic function of finite order
M. V. Kabanko Kursk State University, ul. Radishcheva, 33, Kursk,
305000, Russia
Abstract:
Let f(z) be a meromorphic function on the complex plane of finite order ρ>0. Let ρ(r) be a proximate order in the sense of Boutroux such that lim supr→∞ρ(r)=ρ, lim infr→∞ρ(r)=α>0. If [α]<α⩽ then the types of T(r,f) and |N|(r,f) coincide with respect to \rho(r). If there are integers between \alpha and \rho, then the resulting criterion is formulated in terms of the upper density of zeros and poles of the function f and their argument symmetry.
Keywords:
meromorphic function, function order, function type, upper density, argument symmetry.
Received: 14.11.2022 Accepted: 29.05.2023
Citation:
M. V. Kabanko, “On the type of the meromorphic function of finite order”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 33:2 (2023), 212–224
Linking options:
https://www.mathnet.ru/eng/vuu845 https://www.mathnet.ru/eng/vuu/v33/i2/p212
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Abstract page: | 233 | Full-text PDF : | 68 | References: | 55 |
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