Branched Continued Fraction Expansions of Horn’s Hypergeometric Function H 3 Ratios

Tamara Antonova, Roman Dmytryshyn and Victoriia Kravtsiv
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Tamara Antonova: Institute of Applied Mathematics and Fundamental Sciences, Lviv Polytechnic National University, vul. Stepana Bandery 12, 79000 Lviv, Ukraine
Roman Dmytryshyn: Faculty of Mathematics and Computer Science, Vasyl Stefanyk Precarpathian National University, vul. Shevchenka 57, 76018 Ivano-Frankivsk, Ukraine
Victoriia Kravtsiv: Faculty of Mathematics and Computer Science, Vasyl Stefanyk Precarpathian National University, vul. Shevchenka 57, 76018 Ivano-Frankivsk, Ukraine

Mathematics, 2021, vol. 9, issue 2, 1-18

Abstract: The paper deals with the problem of construction and investigation of branched continued fraction expansions of special functions of several variables. We give some recurrence relations of Horn hypergeometric functions H 3 . By these relations the branched continued fraction expansions of Horn’s hypergeometric function H 3 ratios have been constructed. We have established some convergence criteria for the above-mentioned branched continued fractions with elements in R 2 and C 2 . In addition, it is proved that the branched continued fraction expansions converges to the functions which are an analytic continuation of the above-mentioned ratios in some domain (here domain is an open connected set). Application for some system of partial differential equations is considered.

Keywords: hypergeometric function; branched continued fraction; convergence; continued fraction (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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