The asymptotic form of the Hermite-Padé approximations for a system of mittag-leffler functions

We use the Laplace method for investigation of asymptotic properties of the Hermite integrals. In particular, we find asymptotic form for diagonal Hermite-Padé approximations for a system of exponents. Analogous results are obtained for a system of degenerate hypergeometric functions. These theorems supplement the well-known results of F. Wielinnsky, A. I. Aptekarev and others.