Diophantine approximations using Padé approximations

Abstract

We show how Padé 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 Padé approximations provide exactly Diophantine approximations. Then, we show how Padé approximants to the asymptotic expansion of the remainder term of a value of a series also leads to Diophantine approximation.