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

Authors : Roman Dmytryshyn, Tamara Antonova, Marta Dmytryshyn

Pages : 11-26

Doi:10.33205/cma.1545452

View : 36 | Download : 25

Publication Date : 2024-12-16

Article Type : Research Paper

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