Multidimensional Associated Fractions with Independent Variables and Multiple Power Series

We establish the conditions of existence and uniqueness of a multidimensional associated fraction with independent variables corresponding to a given formal multiple power series and deduce explicit relations for the coefficients of this fraction. The relationship between the multidimensional associ...

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Bibliographic Details
Published in:Ukrainian mathematical journal 2019-08, Vol.71 (3), p.370-386
Main Authors: Bodnar, D. I., Dmytryshyn, R. I.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Applications of Mathematics
Convergence
Domains
Geometry
Independent variables
Mathematical analysis
Mathematics
Mathematics and Statistics
Power series
Statistics
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Summary:We establish the conditions of existence and uniqueness of a multidimensional associated fraction with independent variables corresponding to a given formal multiple power series and deduce explicit relations for the coefficients of this fraction. The relationship between the multidimensional associated fraction and the multidimensional J -fraction with independent variables is demonstrated. The convergence of the multidimensional associated fraction with independent variables is investigated in some domains of the space ℂ N . We construct the expansions of some functions into the corresponding two-dimensional associated fractions with independent variables and demonstrate the efficiency of approximation of the obtained expansions by convergents.
ISSN:0041-5995
1573-9376
DOI:10.1007/s11253-019-01652-5