On the Analytic Continuation of Lauricella–Saran Hypergeometric Function F K ( a 1, a 2, b 1, b 2; a 1, b 2, c 3; z )

Tamara Antonova, Roman Dmytryshyn () and Vitaliy Goran
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Tamara Antonova: Institute of Applied Mathematics and Fundamental Sciences, Lviv Polytechnic National University, 12 Stepan Bandera Str., 79000 Lviv, Ukraine
Roman Dmytryshyn: Faculty of Mathematics and Computer Science, Vasyl Stefanyk Precarpathian National University, 57 Shevchenko Str., 76018 Ivano-Frankivsk, Ukraine
Vitaliy Goran: Faculty of Mathematics and Computer Science, Vasyl Stefanyk Precarpathian National University, 57 Shevchenko Str., 76018 Ivano-Frankivsk, Ukraine

Mathematics, 2023, vol. 11, issue 21, 1-18

Abstract: The paper establishes an analytical extension of two ratios of Lauricella–Saran hypergeometric functions F K 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 F K ( a 1 , a 2 , 1 , b 2 ; a 1 , b 2 , c 3 ; z ) and F K ( a 1 , 1 , b 1 , b 2 ; a 1 , b 2 , c 3 ; z ) to the corresponding branched continued fractions were obtained. To illustrate this, we provide some numerical experiments at the end.

Keywords: Lauricella–Saran hypergeometric function; branched continued fraction; holomorphic functions of several complex variables; analytic continuation; convergence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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