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

V. Hladun (Lviv Polytechnic National University), https://orcid.org/0000-0002-4337-8869
R. Rusyn (Vasyl Stefanyk Precarpathian National University), https://orcid.org/0000-0002-0472-8555
M. Dmytryshyn (West Ukrainian National University), https://orcid.org/0000-0002-0609-9764

Abstract


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.

Keywords


hypergeometric function; continued fraction; holomorphic function of several complex variables; analytic continuation; convergence

MSC 2020


Pri 33C65, Sec 30B70, 32A10, 30B40, 40A99

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References


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DOI: https://doi.org/10.15421/242405

  

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ISSN (Online): 2664-5009
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