SERIES WITH MULTI-VARIABLE LEVELS
Keywords:
Multivariable power series, radius of convergence, Abel's theorem, Cauchy-Adamard formula, Taylor series, holomorphic function, multidimensional analysis.Abstract
This article explores multivariable power series and their properties. The main attention is paid to problems related to the radius of convergence of multidimensional power series, Abel's theorem, Cauchy-Adamard formula, Taylor series expansion, and holomorphic functions. Methods for determining Taylor coefficients in a multivariable case, inequalities for bounded functions, and analytical continuation problems are considered. The study discusses the main theoretical results regarding multidimensional systems of complex analysis.
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