Work

On the analytical continuation of the ratio $H_4(\alpha,\delta+1;\gamma,\delta;-\mathbf{z})/H_4(\alpha,\delta+2;\gamma,\delta+1;-\mathbf{z})$

Year: 2025

Type: article

Abstract: The paper considers the problem of analytical continuation of special functions by branched continued fractions. These representations play an important role in approximating of special functions that arise in various applied problems. By improving the methods of studying the convergence of branched continued fractions, several domains of analytical continuation of the special function $H_4(\alpha,\delta+1;\gamma,\delta;-\mathbf{z})/H_4(\alpha,\delta+2;\gamma,\delta+1;-\mathbf{z})$ in the case of real and complex parameters are established. To prove the analytical continuation, the so-called PC method is used, which is based on the principle of correspondence between a formal double power series and a branched continued fraction. An example is provided at the end.

Source: Researches in Mathematics

DOI: 10.15421/242515

Authors: R. Dmytryshyn, C. Cesarano, I.-A. Lutsiv

Institutions: Vasyl Stefanyk Carpathian National University, UniNettuno University

Language: English

Topic: Mathematical functions and polynomials

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $20

Funders: National Research Foundation of Ukraine, National Research Foundation