Representation of Special Functions by Multidimensional A- and J-Fractions with Independent Variables

The paper deals with the problem of representing special functions by branched continued fractions, particularly multidimensional A- and J-fractions with independent variables, which are generalizations of associated continued fractions and Jacobi continued fractions, respectively. A generalized Gra...

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Bibliographic Details
Published in:Fractal and fractional Vol. 9; no. 2; p. 89
Main Authors: Dmytryshyn, Roman, Sharyn, Serhii
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.02.2025
Subjects:
Algorithms
branched continued fraction
holomorphic functions of several complex variables
Independent variables
multiple power series
numerical approximation
Power series
New York
United States
Ukraine
ISSN:2504-3110, 2504-3110
Online Access:Get full text
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Summary:The paper deals with the problem of representing special functions by branched continued fractions, particularly multidimensional A- and J-fractions with independent variables, which are generalizations of associated continued fractions and Jacobi continued fractions, respectively. A generalized Gragg’s algorithm is constructed that enables us to compute, by the coefficients of the given formal multiple power series, the coefficients of the corresponding multidimensional A- and J-fractions with independent variables. Presented below are numerical experiments for approximating some special functions by these branched continued fractions, which are similar to fractals.
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ISSN:2504-3110
2504-3110
DOI:10.3390/fractalfract9020089