Diophantine approximations using Pade approximations

We show how Pade approximations are used to get Diophantine approximations of real or complex numbers, and so to prove the irrationality. We present two kinds of examples. First, we study two types of series for which Pade approximations provide exactly Diophantine approximations. Then, we show how Pade approximants to the asymptotic expansion of the remainder term of a value of a series also leads to Diophantine approximation. (C) 2000 Elsevier Science B.V. All rights reserved.