On new rational approximants to ζ(3)
arXiv:1204.6712
Abstract
New (infinitely many) rational approximants to ζ(3) proving its irrationality are given. The recurrence relations for the numerator and denominator of these approximants as well as their continued fraction expansions are obtained. A comparison of our approximants with Apéry's approximants to ζ(3) is shown.
This contribution deals with the discovery of infinitely many rational approximants to ζ(3) classified in 12 cases and linked with simultaneous rational approximation problems. Our interest for having infinitely many rational approximants proving the irrationality is motivated by a more deeper question, namely the transcendence of ζ(3), but we are yet uncertain about this question