Numerical stability of branched continued fraction expansions of Appell functions $F_2$ and their ratios in special cases

Roman Dmytryshyn

doi:10.33205/cma.1889392

Numerical stability of branched continued fraction expansions of Appell functions $F_2$ and their ratios in special cases

Abstract

The paper investigates the numerical stability of branched continued fraction expansions of Appell hypergeometric functions $F_2$ and their ratios in special cases. This is important when computing the values of these special functions, as they are widely used in science and engineering. Using the proposed new approach for estimating the so-called tails of approximants of branched continued fraction, we established the sets of numerical stability of the above-mentioned expansions in the cases of real and complex elements. Numerical experiments presented at the end confirm the obtained theoretical results.

Keywords

Project Number

2023.03/0198 "Analysis of the spectra of countably generated algebras of symmetric polynomials and possible applications in quantum mechanics and computer science"

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Details

Primary Language

English

Subjects

Numerical Analysis, Mathematical Methods and Special Functions

Journal Section

Research Article

Authors

Roman Dmytryshyn ^*
0000-0003-2845-0137
Ukraine

Early Pub Date

October 20, 2026

Publication Date

-

Submission Date

February 14, 2026

Acceptance Date

August 25, 2026

Published in Issue

Year 2026 Number: Advanced Online Publication

DOI

https://doi.org/10.33205/cma.1889392

IZ

https://izlik.org/JA37YA44KZ

Cite

RIS / Bibtex

APA

Dmytryshyn, R. (2026). Numerical stability of branched continued fraction expansions of Appell functions $F_2$ and their ratios in special cases. Constructive Mathematical Analysis, Advanced Online Publication, 177-191. https://doi.org/10.33205/cma.1889392

AMA

1.Dmytryshyn R. Numerical stability of branched continued fraction expansions of Appell functions $F_2$ and their ratios in special cases. CMA. 2026;(Advanced Online Publication):177-191. doi:10.33205/cma.1889392

Chicago

Dmytryshyn, Roman. 2026. “Numerical Stability of Branched Continued Fraction Expansions of Appell Functions $F_2$ and Their Ratios in Special Cases”. Constructive Mathematical Analysis, no. Advanced Online Publication: 177-91. https://doi.org/10.33205/cma.1889392.

EndNote

Dmytryshyn R (October 1, 2026) Numerical stability of branched continued fraction expansions of Appell functions $F_2$ and their ratios in special cases. Constructive Mathematical Analysis Advanced Online Publication 177–191.

IEEE

[1]R. Dmytryshyn, “Numerical stability of branched continued fraction expansions of Appell functions $F_2$ and their ratios in special cases”, CMA, no. Advanced Online Publication, pp. 177–191, Oct. 2026, doi: 10.33205/cma.1889392.

ISNAD

Dmytryshyn, Roman. “Numerical Stability of Branched Continued Fraction Expansions of Appell Functions $F_2$ and Their Ratios in Special Cases”. Constructive Mathematical Analysis. Advanced Online Publication (October 1, 2026): 177-191. https://doi.org/10.33205/cma.1889392.

JAMA

1.Dmytryshyn R. Numerical stability of branched continued fraction expansions of Appell functions $F_2$ and their ratios in special cases. CMA. 2026;:177–191.

MLA

Dmytryshyn, Roman. “Numerical Stability of Branched Continued Fraction Expansions of Appell Functions $F_2$ and Their Ratios in Special Cases”. Constructive Mathematical Analysis, no. Advanced Online Publication, Oct. 2026, pp. 177-91, doi:10.33205/cma.1889392.

Vancouver

1.Roman Dmytryshyn. Numerical stability of branched continued fraction expansions of Appell functions $F_2$ and their ratios in special cases. CMA. 2026 Oct. 1;(Advanced Online Publication):177-91. doi:10.33205/cma.1889392