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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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
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Abstract	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.
AbstractList	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.
Author	Goran, Vitaliy Antonova, Tamara Dmytryshyn, Roman
Author_xml	– sequence: 1 givenname: Tamara orcidid: 0000-0002-0358-4641 surname: Antonova fullname: Antonova, Tamara – sequence: 2 givenname: Roman orcidid: 0000-0003-2845-0137 surname: Dmytryshyn fullname: Dmytryshyn, Roman – sequence: 3 givenname: Vitaliy orcidid: 0009-0000-3513-7304 surname: Goran fullname: Goran, Vitaliy
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Cites_doi	10.1002/bimj.4710230709 10.3390/fractalfract6030155 10.15330/cmp.13.3.619-630 10.1103/PhysRevE.53.6297 10.1007/BF03012437 10.3390/axioms11090426 10.1007/BF01902900 10.1007/s10472-023-09831-8 10.1007/JHEP03(2019)083 10.1007/s40315-021-00377-6 10.3390/math9020148 10.1002/bimj.4710210605 10.1090/mmono/110 10.1007/s10958-022-06062-w 10.1007/s10958-020-04729-w 10.1016/j.jmaa.2021.125439 10.1007/s11253-023-02138-1 10.1088/0305-4470/31/8/008 10.15330/cmp.13.3.592-607 10.30970/ms.52.2.115-123 10.1080/00949659508811629 10.3390/axioms12030299
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Copyright_xml	– notice: 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
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SubjectTerms	analytic continuation branched continued fraction convergence holomorphic functions of several complex variables Hypergeometric functions Lauricella–Saran hypergeometric function Neighborhoods Polyvinylidene chlorides Power series
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Title	On the Analytic Continuation of Lauricella–Saran Hypergeometric Function FK(a1,a2,b1,b2;a1,b2,c3;z)
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