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.
Keywords:multidimensional number series, multidimensional functional series, reduction to a one-dimensional series, convergence, uniform convergence, examples
Fulltext:
PDF file (901 kB)
The content is published under the terms of the Creative Commons Attribution 4.0 International License
