Hoienko N. Lauricella Hypergeometric Functions Approximation with Branched Continued Fractions.

New recursion relations of Lauricella hypergeometric functions FD are established in the thesis. On this base the expansions of these functions into branched continued fractions are built, in particular the multidimensional analogue of Norlund continued fraction is built; for the first time the criterions of convergence of branched continued fractions being the expansions of Lauricella hypergeometric functions are established; the regions of convergence, uniform convergence of these fractions are investigated, there are found the estimations of approximation errors for fraction approximants; for the first time there is established the multidimensional analogue of Norlund theorem on the convergence and compliance of continuous fraction that is expansion of Gauss functions ratio; the Norlund type branched continuous fractions convergence to function being analitical continuation of Lauricella functions ratio is proved.