On Analytical Continuation of the Horn’s Hypergeometric Functions <i>H</i><sub>3</sub> and Their Ratios

On Analytical Continuation of the Horn’s Hypergeometric Functions <i>H</i><sub>3</sub> and Their Ratios

This paper considers the Horn’s hypergeometric function <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>H</mi><mn>3</mn></msub></semantics></math></inline-f...

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Bibliographic Details
Main Authors: Roman Dmytryshyn, Tamara Antonova, Sofiia Hladun
Format: Article
Language:English
Published: MDPI AG 2025-01-01
Series:Axioms
Subjects:
hypergeometric function
branched continued fraction
analytical continuation
convergence
approximation by rational functions
Online Access:https://www.mdpi.com/2075-1680/14/1/67
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Summary:This paper considers the Horn’s hypergeometric function <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>H</mi><mn>3</mn></msub></semantics></math></inline-formula>, which is closely related to other hypergeometric functions and has various mathematical or physical applications. The problem of analytical extension of this function is solved using a special family of functions—branched continued fractions. A new domain of analytical extension of the Horn’s hypergeometric functions <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>H</mi><mn>3</mn></msub></semantics></math></inline-formula> and their ratios under certain conditions to real parameters are established. This paper also contains an example of the presentation and continuation of some special function and an analysis of numerical results.
ISSN:2075-1680

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