A new proof of the irrationality of (2) and (3) using Padé approximants

摘要

Using Padé approximants to the asymptotic expansion of the error term for the series , , and , we recover Apéry's sequences which allow one to prove the irrationality of (2) and of (3). The same method applied to the partial sums of ln(1 ? t) also proves the irrationality of certain values of the logarithm.