Researches in Mathematics (Dec 2023)

On the domains of convergence of the branched continued fraction expansion of ratio $H_4(a,d+1;c,d;\mathbf{z})/H_4(a,d+2;c,d+1;\mathbf{z})$

  • R.I. Dmytryshyn,
  • I.-A.V. Lutsiv,
  • O.S. Bodnar

DOI
https://doi.org/10.15421/242311
Journal volume & issue
Vol. 31, no. 2
pp. 19 – 25

Abstract

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The paper considers the problem of establishing the convergence criteria of the branched continued fraction expansion of the ratio of Horn's hypergeometric functions $H_4$. To solve it, the technique of expanding the domain of convergence of the branched continued fraction from the known small domain of convergence to a wider domain of convergence is used. For the real and complex parameters of the Horn hypergeometric function $H_4$, a number of convergence criteria of the branched continued fraction expansion under certain conditions to its coefficients in various unbounded domains of the space have been established.

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