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  4. On convergence of function F4(1,2;2,2;z1,z2) expansion into a branched continued fraction

On convergence of function F4(1,2;2,2;z1,z2) expansion into a branched continued fraction

MMC.
2022;
Volume 9, Number 3
: pp. 767–778
https://doi.org/10.23939/mmc2022.03.767
Received: February 02, 2022
Revised: September 15, 2022
Accepted: September 16, 2022

Mathematical Modeling and Computing, Vol. 9, No. 3, pp. 767–778 (2022)

Authors:
  1. V. R. Hladun
  2. N. P. Hoyenko
  3. O. S. Manziy
  4. L. S. Ventyk
1
Lviv Polytechnic National University
2
Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine
3
Lviv Polytechnic National University
4
Lviv Polytechnic National University

In the paper, the possibility of the Appell hypergeometric function ${F_4}(1,2; 2,2;{z_1},{z_2})$ approximation by a branched continued fraction of a special form is analysed.  The correspondence of the constructed branched continued fraction to the Appell hypergeometric function $F_4$ is proved.  The convergence of the obtained branched continued fraction in some polycircular domain of two-dimensional complex space is established, and numerical experiments are carried out.  The results of the calculations confirmed the efficiency of approximating the Appell hypergeometric function ${F_4}(1,2;2,2;{z_1},{z_2})$ by a branched continued fraction of special form and illustrated the hypothesis of the existence of a wider domain of convergence of the obtained  expansion.

hypergeometric series
Appell hypergeometric function
recurrence relation
continued fraction
branched continued fraction
convergence domain
correspondence
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