Work

Research on the convergence of some types of functional branched continued fractions

Year: 2024

Type: article

Abstract: An analysis of research on the problem of convergence of various types of functional branched continued fractions has been carried out. Branched continued fractions with $N$ branching branches and branched continued fractions with independent variables are considered. The definition and, in our opinion, characteristic criteria of convergence of multidimensional generalizations of C-, S-, g-, J-fractions are given, both for branched continued fractions of the general form with $N$ branching branches and branched continued fractions with independent variables. Such multidimensional generalizations of continued fractions arise, in particular, in the development of various classes of hypergeometric functions of several variables, in particular, the functions of Appel, Lauricella, Horn, etc.

Source: Carpathian Mathematical Publications

DOI: 10.15330/cmp.16.2.448-460

Authors: D.I. Bodnar, O.S. Bodnar, M.V. Dmytryshyn, M.M. Popov, M.V. Martsinkiv, O.B. Salamakha

Institutions: West Ukrainian National University, Ternopil Volodymyr Hnatiuk National Pedagogical University, Uniwersytet Pomorski w Słupsku, Vasyl Stefanyk Carpathian National University

Language: English

Topic: Mathematical functions and polynomials

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4403362623

FWCI: 8.59

Cites:

Cited by: 11

Related to: 10