On the analytic extension of three ratios of Horn's confluent hypergeometric function $\mathrm{H}_7$
| Autor: | V. Hladun, R. Rusyn, M. Dmytryshyn |
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| Jazyk: | English<br />Ukrainian |
| Rok vydání: | 2024 |
| Předmět: | |
| Zdroj: | Researches in Mathematics, Vol 32, Iss 1, Pp 60-70 (2024) |
| Druh dokumentu: | article |
| ISSN: | 2664-4991 2664-5009 |
| DOI: | 10.15421/242405 |
| Popis: | 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. |
| Databáze: | Directory of Open Access Journals |
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