On the Analytic Continuation of Lauricella–Saran Hypergeometric Function FK(a1,a2,b1,b2;a1,b2,c3;z)-Reference-Cited by-同舟云学术

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

Published:2023-10-30 Issue:21 Volume:11 Page:4487
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Antonova Tamara¹^ORCID,Dmytryshyn Roman²^ORCID,Goran Vitaliy²^ORCID

Affiliation:

1. Institute of Applied Mathematics and Fundamental Sciences, Lviv Polytechnic National University, 12 Stepan Bandera Str., 79000 Lviv, Ukraine

2. Faculty of Mathematics and Computer Science, Vasyl Stefanyk Precarpathian National University, 57 Shevchenko Str., 76018 Ivano-Frankivsk, Ukraine

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.

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Link

https://www.mdpi.com/2227-7390/11/21/4487/pdf

Reference39 articles.

1. Erdélyi, A., Magnus, W., Oberhettinger, F., and Tricomi, F.G. (1953). Higher Transcendental Functions, Volume 1, McGraw-Hill Book Co.

2. Erdélyi, A., Magnus, W., Oberhettinger, F., and Tricomi, F.G. (1953). Higher Transcendental Functions, Volume 2, McGraw-Hill Book Co.

3. Erdélyi, A., Magnus, W., Oberhettinger, F., and Tricomi, F.G. (1955). Higher Transcendental Functions, Volume 3, McGraw-Hill Book Co.

4. Horwood, E. (1976). Multiple Hypergeometric Functions and Applications, Halsted Press.

5. Srivastava, H.M., and Karlsson, P.W. (1985). Multiple Gaussian Hypergeometric Series, Halsted Press.

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