Analysis shows a new domain for analytic continuation of special functions, suggesting broader applications to mathematical functions.
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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Marta Dmytryshyn (2025) studied this question.
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