Treffer: On the analytical continuation of the ratio $H_4(\alpha,\delta+1;\gamma,\delta;-\mathbf{z})/H_4(\alpha,\delta+2;\gamma,\delta+1;-\mathbf{z})$

Title:
On the analytical continuation of the ratio $H_4(\alpha,\delta+1;\gamma,\delta;-\mathbf{z})/H_4(\alpha,\delta+2;\gamma,\delta+1;-\mathbf{z})$
Authors:
R. Dmytryshyn, C. Cesarano, I.-A. Lutsiv
Source:
Researches in Mathematics, Vol 33, Iss 2, Pp 65-76 (2025)
Publisher Information:
Oles Honchar Dnipro National University, 2025.
Publication Year:
2025
Collection:
LCC:Mathematics
Subject Terms:
hypergeometric function, branched continued fraction, analytic function, approximation by rational functions, convergence, analytic continuation, Mathematics, QA1-939
Document Type:
Fachzeitschrift article
File Description:
electronic resource
Language:
English
ISSN:
2664-4991
2664-5009
Relation:
https://vestnmath.dnu.dp.ua/index.php/rim/article/view/464/464; https://doaj.org/toc/2664-4991; https://doaj.org/toc/2664-5009
DOI:
10.15421/242515
Access URL:
https://doaj.org/article/e011183c3669435bbfe74ea36daaabe3
Accession Number:
edsdoj.011183c3669435bbfe74ea36daaabe3
Database:
Directory of Open Access Journals

Weitere Informationen

The paper considers the problem of analytical continuation of special functions by branched continued fractions. These representations play an important role in approximating of special functions that arise in various applied problems. By improving the methods of studying the convergence of branched continued fractions, several domains of analytical continuation of the special function $H_4(\alpha,\delta+1;\gamma,\delta;-\mathbf{z})/H_4(\alpha,\delta+2;\gamma,\delta+1;-\mathbf{z})$ in the case of real and complex parameters are established. To prove the analytical continuation, the so-called PC method is used, which is based on the principle of correspondence between a formal double power series and a branched continued fraction. An example is provided at the end.