4.7 Article

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

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MATHEMATICS
卷 11, 期 21, 页码 -

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MDPI
DOI: 10.3390/math11214487

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Lauricella-Saran hypergeometric function; branched continued fraction; holomorphic functions of several complex variables; analytic continuation; convergence

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This paper establishes an analytical extension of the ratios of Lauricella-Saran hypergeometric functions F-K to the corresponding branched continued fractions. The results are further validated through numerical experiments.
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 FK(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.

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