Journal of Integer Sequences, Vol. 8 (2005), Article 05.1.1

Beukers' integrals and Apéry's recurrences

Lalit Jain
Faculty of Mathematics
University of Waterloo
Waterloo, Ontario N2L 3G1
CANADA

Pavlos Tzermias
Department of Mathematics
University of Tennessee
Knoxville, TN 37996-1300
USA

Abstract: We give a new and completely elementary proof of the fact that the rational approximations to π² obtained by Apéry in his famous proof of the irrationality of certain values of the Riemann zeta function are identical to those obtained by Beukers in one of his alternative proofs of Apéry's result.

(Concerned with sequence A005285 .)

Received September 6 2004; revised version received January 3 2005. Published in Journal of Integer Sequences January 10 2005.