On the analytic extension of the Horn's hypergeometric function $H_4$

Authors

  • R. Dmytryshyn Vasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, Ukraine
  • I.-A. Lutsiv Vasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, Ukraine
  • M. Dmytryshyn West Ukrainian National University, 11 Lvivska str., 46009, Ternopil, Ukraine
https://doi.org/10.15330/cmp.16.1.32-39

Keywords:

branched continued fraction, Horn hypergeometric function, approximation by rational functions, convergence, analytic continuation
Published online: 2024-04-02

Abstract

The paper establishes new convergence domains of branched continued fraction expansions of Horn's hypergeometric function $H_4$ with real and complex parameters. These domains enabled the PC method to establish the analytical extension of analytical functions to their expansions in the studied domains of convergence. A few examples are provided at the end to illustrate this.

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How to Cite
(1)
Dmytryshyn, R.; Lutsiv, I.-A.; Dmytryshyn, M. On the Analytic Extension of the Horn’s Hypergeometric Function $H_4$. Carpathian Math. Publ. 2024, 16, 32-39.