Branched Continued Fraction Expansions of Horn’s Hypergeometric Function H3 Ratios

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 H3. By these relations the branched continued fraction expansions of Horn’s hyper...

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Bibliographic Details
Published in:Mathematics (Basel) Vol. 9; no. 2; p. 148
Main Authors: Antonova, Tamara, Dmytryshyn, Roman, Kravtsiv, Victoriia
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.01.2021
Subjects:
branched continued fraction
Computational mathematics
continued fraction
Convergence
Domains
hypergeometric function
Hypergeometric functions
Mathematical analysis
Mathematics
Partial differential equations
Ratios
ISSN:2227-7390, 2227-7390
Online Access:Get full text
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Summary: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 H3. By these relations the branched continued fraction expansions of Horn’s hypergeometric function H3 ratios have been constructed. We have established some convergence criteria for the above-mentioned branched continued fractions with elements in R2 and C2. 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.
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ISSN:2227-7390
2227-7390
DOI:10.3390/math9020148