Email this article One way of summing multidimensional series
- Authors: Sabitov K.B.1
-
Affiliations:
- Sterlitamak Branch of the Ufa University of Science and Technology
- Issue: Vol 27, No 4 (2023)
- Pages: 745-752
- Section: Short Communications
- URL: https://journals.rcsi.science/1991-8615/article/view/311005
- DOI: https://doi.org/10.14498/vsgtu2069
- EDN: https://elibrary.ru/UMYSET
- ID: 311005
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Abstract
It is known that in analysis courses, multiple series are considered only at a conceptual level, and their simplest properties are provided. Two widely used methods for summing multiple Fourier series are the spherical and rectangular methods. The present study is devoted to a new method of proving the convergence of multidimensional series by reducing them to a one-dimensional series, allowing applicating known statements for one-dimensional series to multidimensional ones. Examples of justifying the convergence of numerical and functional series are provided as an illustration of this summing method.
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##article.viewOnOriginalSite##About the authors
Kamil B. Sabitov
Sterlitamak Branch of the Ufa University of Science and Technology
Author for correspondence.
Email: sabitov_fmf@mail.ru
ORCID iD: 0000-0001-9516-2704
http://www.mathnet.ru/person11101
Dr. Phys. & Math. Sci., Professor; Senior Researcher; Sector of Basic Scientific Research
Russian Federation, 453103, Sterlitamak, Lenin Ave., 49References
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