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Fractal Fract
Volume 9
Issue 2
10.3390/fractalfract9020089
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Article

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

by
Roman Dmytryshyn
* and
Serhii Sharyn
Faculty of Mathematics and Computer Science, Vasyl Stefanyk Precarpathian National University, 57 Shevchenko Str., 76018 Ivano-Frankivsk, Ukraine
*
Author to whom correspondence should be addressed.
Fractal Fract. 2025, 9(2), 89; https://doi.org/10.3390/fractalfract9020089
Submission received: 31 December 2024 / Revised: 26 January 2025 / Accepted: 26 January 2025 / Published: 28 January 2025
Versions Notes

Abstract

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.
Keywords: branched continued fraction; multiple power series; holomorphic functions of several complex variables; numerical approximation branched continued fraction; multiple power series; holomorphic functions of several complex variables; numerical approximation

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MDPI and ACS Style

Dmytryshyn, R.; Sharyn, S. Representation of Special Functions by Multidimensional A- and J-Fractions with Independent Variables. Fractal Fract. 2025, 9, 89. https://doi.org/10.3390/fractalfract9020089

AMA Style

Dmytryshyn R, Sharyn S. Representation of Special Functions by Multidimensional A- and J-Fractions with Independent Variables. Fractal and Fractional. 2025; 9(2):89. https://doi.org/10.3390/fractalfract9020089

Chicago/Turabian Style

Dmytryshyn, Roman, and Serhii Sharyn. 2025. "Representation of Special Functions by Multidimensional A- and J-Fractions with Independent Variables" Fractal and Fractional 9, no. 2: 89. https://doi.org/10.3390/fractalfract9020089

APA Style

Dmytryshyn, R., & Sharyn, S. (2025). Representation of Special Functions by Multidimensional A- and J-Fractions with Independent Variables. Fractal and Fractional, 9(2), 89. https://doi.org/10.3390/fractalfract9020089

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