December 2, 2025Open Access

On the Domain of Analytical Continuation of the Ratios of Generalized Hypergeometric Functions 3F2

MDMarta DmytryshynUniversity of Wisconsin System

Key Points

Establishes a new domain for analytic continuation of generalized hypergeometric functions.
Finds that the domain of convergence relates closely to the branched continued fraction expansion.
Analysis of the special function under specific parameter conditions supports the findings.
Implications for the dilogarithm function highlight the results' relevance in advanced mathematical contexts.

Abstract

The paper considers the problem of the analytical extension of the ratios of generalized hypergeometric functions 3F2. A new domain of analytic continuation for these ratios under certain conditions to parameters is established. In this case, the domain of analytic extension of the special function is the domain of convergence of its branched continued fraction expansion. This paper also provides an example of applying the obtained results to dilogarithm function.

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Cite This Study

Marta Dmytryshyn (Thu,) studied this question.

synapsesocial.com/papers/692e3d846c9b3ab28c18749d https://doi.org/https://doi.org/10.3390/axioms14120871