On Analytical Extension of Generalized Hypergeometric Function 3F2 - Roman Dmytryshyn; Volodymyra Oleksyn (Axioms)
The paper considers the generalized hypergeometric function <semantics><mmultiscripts>F2<none></none><mprescripts></mprescripts>3<none></none></mmultiscripts>,</semantics> which is important in various fields of mathematics, physics, and economics. The method is used, according to which the domains of the analytical continuation of the special functions are the domains of convergence of their expansions into a special family of functions, namely branched continued fractions. These expansions have wide domains of convergence and better computational properties, particularly compared with series, making them effective tools for representing special functions. New domains of the analytical continuation of the generalized hypergeometric function <semantics><mmultiscripts>F2<none></none><mprescripts></mprescripts>3<none></none></mmultiscripts></semantics> with real and complex parameters have been established. The paper also includes examples of the presentation and extension of some special functions.