Chernetska L. Generalized moment representations and rational approximants of many-variables functions

The problems of the construction Pade type approximants for functions of several variables by using the method of generalized moment representations are investigated. V.K. Dzyadyk's method of generalized moment presentations is extended to the multidimensional case. The theorems on the construction of rational approximants for power series of several variables are established. Pade type approximants for a wide class of functions of two and several variables, particularly for Appel, Humbert and Lauricella hypergeometric series are constructed and investigated. Convergence is proved and asymptotic equalities for numerators and denominators of Pade type approximants for Humbert series are established.