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 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.

Automated summary

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.