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ЖУРНАЛЫ // Проблемы анализа — Issues of Analysis // Архив

Пробл. анал. Issues Anal., 2024, том 13(31), выпуск 3, страницы 56–63 (Mi pa407)

On calculating sums of some double series

V. I. Kuzovatov, A. S. Bushkova

Siberian Federal University, 79 Svobodnyi pr., Krasnoyarsk 660041, Russia

Аннотация: We consider systems of two equations consisting of a polynomial and an entire function. By calculating the resultant of the polynomial and the entire function in two different ways, we can obtain a relation for double numerical series. The formula of A. M. Kytmanov and E. K. Myshkina was used as the first method for calculating the resultant. For the second method, we chose the formula for product of values of one function in the roots of another. A family of sums of some types of double numerical series absent in known references was found. We also demonstrate an approach to finding sums of lower dimension (one-dimensional sums) that arise when calculating the resultant of the original system of functions.

Ключевые слова: sum of double numerical series, resultant, entire function.

УДК: 517.5

MSC: 30C15, 13P15

Поступила в редакцию: 22.08.2024
Исправленный вариант: 30.10.2024
Принята в печать: 30.10.2024

Язык публикации: английский

DOI: 10.15393/j3.art.2024.16959



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