On the Analytic Extension of Lauricella–Saran’s Hypergeometric Function FK to Symmetric Domains

In this paper, we consider the representation and extension of the analytic functions of three variables by special families of functions, namely branched continued fractions. In particular, we establish new symmetric domains of the analytical continuation of Lauricella–Saran’s hypergeometric functi...

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Bibliographic Details
Published in:Symmetry (Basel) Vol. 16; no. 2; p. 220
Main Authors: Dmytryshyn, Roman, Goran, Vitaliy
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.02.2024
Subjects:
Analytic functions
Convergence
Domains
Fractions
Hypergeometric functions
Mathematical analysis
Polyvinylidene chlorides
Representations
ISSN:2073-8994, 2073-8994
Online Access:Get full text
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Summary:In this paper, we consider the representation and extension of the analytic functions of three variables by special families of functions, namely branched continued fractions. In particular, we establish new symmetric domains of the analytical continuation of Lauricella–Saran’s hypergeometric function FK with certain conditions on real and complex parameters using their branched continued fraction representations. We use a technique that extends the convergence, which is already known for a small domain, to a larger domain to obtain domains of convergence of branched continued fractions and the PC method to prove that they are also domains of analytical continuation. In addition, we discuss some applicable special cases and vital remarks.
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ISSN:2073-8994
2073-8994
DOI:10.3390/sym16020220