Abstract
We use the Laplace method for investigation of asymptotic properties of the Hermite integrals. In particular, we find asymptotic form for diagonal Hermite-Pade 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.
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