On the Analytic Continuation of Lauricella–Saran Hypergeometric Function FK(a1,a2,b1,b2;a1,b2,c3;z)

The paper establishes an analytical extension of two ratios of Lauricella–Saran hypergeometric functions FK with some parameter values to the corresponding branched continued fractions in their domain of convergence. The PC method used here is based on the correspondence between a formal triple powe...

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Bibliographic Details
Published in:Mathematics (Basel) Vol. 11; no. 21; p. 4487
Main Authors: Antonova, Tamara, Dmytryshyn, Roman, Goran, Vitaliy
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.11.2023
Subjects:
analytic continuation
branched continued fraction
convergence
holomorphic functions of several complex variables
Hypergeometric functions
Lauricella–Saran hypergeometric function
Neighborhoods
Polyvinylidene chlorides
Power series
ISSN:2227-7390, 2227-7390
Online Access:Get full text
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Summary:The paper establishes an analytical extension of two ratios of Lauricella–Saran hypergeometric functions FK with some parameter values to the corresponding branched continued fractions in their domain of convergence. The PC method used here is based on the correspondence between a formal triple power series and a branched continued fraction. As additional results, analytical extensions of the Lauricella–Saran hypergeometric functions FK(a1,a2,1,b2;a1,b2,c3;z) and FK(a1,1,b1,b2;a1,b2,c3;z) to the corresponding branched continued fractions were obtained. To illustrate this, we provide some numerical experiments at the end.
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ISSN:2227-7390
2227-7390
DOI:10.3390/math11214487