On Some Branched Continued Fraction Expansions for Horn’s Hypergeometric Function H4(a,b;c,d;z1,z2) Ratios

The paper deals with the problem of representation of Horn’s hypergeometric functions by branched continued fractions. The formal branched continued fraction expansions for three different Horn’s hypergeometric function H4 ratios are constructed. The method employed is a two-dimensional generalizati...

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Bibliographic Details
Published in:Axioms Vol. 12; no. 3; p. 299
Main Authors: Antonova, Tamara, Dmytryshyn, Roman, Lutsiv, Ilona-Anna, Sharyn, Serhii
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.03.2023
Subjects:
Analytic functions
branched continued fraction
Computational mathematics
convergence
Domains
holomorphic functions of several complex variables
Horn function
Horns
Hypergeometric functions
Mathematical analysis
numerical approximation
Partial differential equations
Ratios
ISSN:2075-1680, 2075-1680
Online Access:Get full text
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Summary:The paper deals with the problem of representation of Horn’s hypergeometric functions by branched continued fractions. The formal branched continued fraction expansions for three different Horn’s hypergeometric function H4 ratios are constructed. The method employed is a two-dimensional generalization of the classical method of constructing of Gaussian continued fraction. It is proven that the branched continued fraction, which is an expansion of one of the ratios, uniformly converges to a holomorphic function of two variables on every compact subset of some domain H,H⊂C2, and that this function is an analytic continuation of this ratio in the domain H. The application to the approximation of functions of two variables associated with Horn’s double hypergeometric series H4 is considered, and the expression of solutions of some systems of partial differential equations is indicated.
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ISSN:2075-1680
2075-1680
DOI:10.3390/axioms12030299