On the Regular Variation of Main Characteristics of an Entire Function
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...
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| Datum: | 2003 |
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| Format: | Artikel |
| Sprache: | Ukrainisch Englisch |
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Institute of Mathematics, NAS of Ukraine
2003
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/3958 |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510089821028352 |
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| author | Filevych, P. V. Sheremeta, M. M. Філевич, П. В. Шеремета, М. М. |
| author_facet | Filevych, P. V. Sheremeta, M. M. Філевич, П. В. Шеремета, М. М. |
| author_sort | Filevych, P. V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:16:01Z |
| description | 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. |
| first_indexed | 2026-03-24T02:51:27Z |
| format | Article |
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| id | umjimathkievua-article-3958 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T02:51:27Z |
| publishDate | 2003 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/0f/06c007dd593385c7a0d6d1899a84f80f.pdf |
| spelling | umjimathkievua-article-39582020-03-18T20:16:01Z On the Regular Variation of Main Characteristics of an Entire Function Про правильну зміну основних характеристик цілої функції Filevych, P. V. Sheremeta, M. M. Філевич, П. В. Шеремета, М. М. 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. Встановлено необхідну і достатню умову на коефіцієнти a n цілої фуіікції \(f(z) = \sum {_{n = 0}^\infty } {\text{ }}a_n z^n \) для того, щоб її центральний індекс і логарифми максимуму модуля та максимального члена були правильно змінними функціями. Побудовано цілу функцію, логарифм максимуму модуля якої — правильно змінна функція, а характеристична функція Неванлінии не є правильно змінною функцією. Institute of Mathematics, NAS of Ukraine 2003-06-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/3958 Ukrains’kyi Matematychnyi Zhurnal; Vol. 55 No. 6 (2003); 840-849 Український математичний журнал; Том 55 № 6 (2003); 840-849 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/3958/4628 https://umj.imath.kiev.ua/index.php/umj/article/view/3958/4629 Copyright (c) 2003 Filevych P. V.; Sheremeta M. M. |
| spellingShingle | Filevych, P. V. Sheremeta, M. M. Філевич, П. В. Шеремета, М. М. On the Regular Variation of Main Characteristics of an Entire Function |
| title | On the Regular Variation of Main Characteristics of an Entire Function |
| title_alt | Про правильну зміну основних характеристик цілої
функції |
| title_full | On the Regular Variation of Main Characteristics of an Entire Function |
| title_fullStr | On the Regular Variation of Main Characteristics of an Entire Function |
| title_full_unstemmed | On the Regular Variation of Main Characteristics of an Entire Function |
| title_short | On the Regular Variation of Main Characteristics of an Entire Function |
| title_sort | on the regular variation of main characteristics of an entire function |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/3958 |
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