ON CALCULATING SUMS OF SOME DOUBLE SERIES
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...
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| Format: | Article |
| Language: | English |
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Petrozavodsk State University
2024-11-01
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| Series: | Проблемы анализа |
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| Online Access: | https://issuesofanalysis.petrsu.ru/article/genpdf.php?id=16959&lang=en |
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| author | V. I. Kuzovatov A. S. Bushkova |
| author_facet | V. I. Kuzovatov A. S. Bushkova |
| author_sort | V. I. Kuzovatov |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-ba51f02788ab4d3fbc8277ab13c30d6b |
| institution | Kabale University |
| issn | 2306-3424 2306-3432 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | Petrozavodsk State University |
| record_format | Article |
| series | Проблемы анализа |
| spelling | doaj-art-ba51f02788ab4d3fbc8277ab13c30d6b2025-01-28T10:50:36ZengPetrozavodsk State UniversityПроблемы анализа2306-34242306-34322024-11-0113 (31)3566310.15393/j3.art.2024.16959ON CALCULATING SUMS OF SOME DOUBLE SERIESV. I. Kuzovatov0A. S. Bushkova1Siberian Federal UniversitySiberian Federal UniversityWe 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.https://issuesofanalysis.petrsu.ru/article/genpdf.php?id=16959&lang=ensum of double numerical seriesresultantentire function |
| spellingShingle | V. I. Kuzovatov A. S. Bushkova ON CALCULATING SUMS OF SOME DOUBLE SERIES Проблемы анализа sum of double numerical series resultant entire function |
| title | ON CALCULATING SUMS OF SOME DOUBLE SERIES |
| title_full | ON CALCULATING SUMS OF SOME DOUBLE SERIES |
| title_fullStr | ON CALCULATING SUMS OF SOME DOUBLE SERIES |
| title_full_unstemmed | ON CALCULATING SUMS OF SOME DOUBLE SERIES |
| title_short | ON CALCULATING SUMS OF SOME DOUBLE SERIES |
| title_sort | on calculating sums of some double series |
| topic | sum of double numerical series resultant entire function |
| url | https://issuesofanalysis.petrsu.ru/article/genpdf.php?id=16959&lang=en |
| work_keys_str_mv | AT vikuzovatov oncalculatingsumsofsomedoubleseries AT asbushkova oncalculatingsumsofsomedoubleseries |