Work

On the analytic extension of the Horn's confluent function $\mathrm{H}_6$ on domain in the space $\mathbb{C}^2$

Year: 2024

Type: article

Abstract: The paper considers the problem of representation and extension of Horn's confluent functions by a special family of functions - branched continued fractions. In a new region, an estimate of the rate of convergence for branched continued fraction expansions of the ratios of Horn's confluent functions $\mathrm{H}_6$ with real parameters is established. Here, region is a domain (open connected set) together with all, part or none of its boundary. Also, a new domain of the analytical continuation of the above-mentioned ratios is established, using their branched continued fraction expansions whose elements are polynomials in the space $\mathbb{C}^2$. These expansions can be used to approximate the solutions of certain differential equations and analytic functions, which are represented by the Horn's confluent functions $\mathrm{H}_6.$

Source: Constructive Mathematical Analysis

DOI: 10.33205/cma.1545452

Authors: Roman Dmytryshyn, Tamara Antonova, Marta Dmytryshyn

Institutions: Vasyl Stefanyk Carpathian National University, Lviv Polytechnic National University, West Ukrainian National University

Language: English

Topic: Mathematical functions and polynomials

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4405419503

FWCI: 6.121

Cites: 27

Cited by: 8

Related to: 10