On the Analytic Continuation of Appell’s Hypergeometric Function F2 to Some Symmetric Domains in the Space C2
Year: 2024
Type: article
Abstract: The paper considers the problem of representation and extension of Appell’s hypergeometric functions by a special family of functions—branched continued fractions. Here, we establish new symmetric domains of the analytical continuation of Appell’s hypergeometric function F2 with real and complex parameters, using their branched continued fraction expansions whose elements are polynomials in the space C2. To do this, we used a technique that extends the domain of convergence of the branched continued fraction, which is already known for a small domain, to a larger domain, as well as the PC method to prove that it is also the domain of analytical continuation. A few examples are provided at the end to illustrate this.
Source: Symmetry
DOI: 10.3390/sym16111480
Author: Roman Dmytryshyn
Institution: Vasyl Stefanyk Carpathian National University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,728
OpenAlex ID: W4404114710