Work

On the analytic extension of three ratios of Horn's confluent hypergeometric function $\mathrm{H}_7$

Year: 2024

Type: article

Abstract: In this paper, we consider the extension of the analytic functions of two variables by special families of functions — continued fractions. In particular, we establish new symmetric domains of the analytical continuation of three ratios of Horn's confluent hypergeometric function $\mathrm{H}_7$ with certain conditions on real and complex parameters using their continued fraction representations. We use Worpitzky's theorem, the multiple parabola theorem, and a technique that extends the convergence, already known for a small domain, to a larger domain to obtain domains of convergence of continued fractions, and the PC method to prove that they are also domains of analytical continuation.

Source: Researches in Mathematics

DOI: 10.15421/242405

Authors: V. Hladun, R. Rusyn, M. Dmytryshyn

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

Language: English

Topic: Mathematical functions and polynomials

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $20

OpenAlex ID: W4400510744

FWCI: 6.848

Cites: 1

Cited by: 22

Related to: 10