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

Year 2024, Volume: 7 Issue: Special Issue: AT&A, 11 - 26, 16.12.2024

Roman Dmytryshyn , Tamara Antonova , Marta Dmytryshyn

https://doi.org/10.33205/cma.1545452

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 $\mathrm{H}_6.$

Keywords

Horn, branched continued fraction, holomorphic functions of several complex variables, analytic continuation, convergence

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