Geodesic
One way of summing multidimensional series
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 27 (2023) no. 4, pp. 745-752

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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.
Keywords: multidimensional number series, multidimensional functional series, reduction to a one-dimensional series, examples
Mots-clés : convergence, uniform convergence 
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     title = {One way of summing multidimensional series},
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K. B. Sabitov. One way of summing multidimensional series. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 27 (2023) no. 4, pp. 745-752. http://geodesic.mathdoc.fr/item/VSGTU_2023_27_4_a8/