Branched Continued Fraction Expansions of Horn's Hypergeometric Function H3 Ratios

The paper deals with the problem of construction and investigation of branched continued fraction expansions of special functions of several variables. We give some recurrence relations of Horn hypergeometric functions H-3. By these relations the branched continued fraction expansions of Horn's hypergeometric function H-3 ratios have been constructed. We have established some convergence criteria for the above-mentioned branched continued fractions with elements in R-2 and C-2. In addition, it is proved that the branched continued fraction expansions converges to the functions which are an analytic continuation of the above-mentioned ratios in some domain (here domain is an open connected set). Application for some system of partial differential equations is considered.

Automated summary

This paper discusses the construction and investigation of branched continued fraction expansions of special functions of several variables, particularly focusing on the Horn hypergeometric function H-3. Recurrence relations are provided for H-3, leading to the construction of branched continued fraction expansions for H-3 ratios. Convergence criteria are established for these fractions in both real and complex domains, with proof of convergence to the functions' analytic continuations in certain domains and consideration of applications to systems of partial differential equations.