On the analytic extension of three ratios of Horn's confluent hypergeometric function $\mathrm{H}_7

In this paper, we consider the extension of the analytic functions of two variables by special families of functions — continued fractions. In particular, we establish new symmetric domains of the analytical continuation of three ratios of Horn's confluent hypergeometric function $\mathrm{H}_7$...

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Bibliographic Details
Published in:Researches in mathematics (Online) 2024-07, Vol.32 (1), p.60-70
Main Authors: Hladun, V., Rusyn, R., Dmytryshyn, M.
Format: Article
Language:English
Subjects:
analytic continuation
continued fraction
convergence
holomorphic function of several complex variables
hypergeometric function
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Summary:In this paper, we consider the extension of the analytic functions of two variables by special families of functions — continued fractions. In particular, we establish new symmetric domains of the analytical continuation of three ratios of Horn's confluent hypergeometric function $\mathrm{H}_7$ with certain conditions on real and complex parameters using their continued fraction representations. We use Worpitzky's theorem, the multiple parabola theorem, and a technique that extends the convergence, already known for a small domain, to a larger domain to obtain domains of convergence of continued fractions, and the PC method to prove that they are also domains of analytical continuation.
ISSN:2664-4991
2664-5009
DOI:10.15421/242405