On the irrationality of certain series

Paul Erdős and Ernst Gabor Straus

Vol. 55 (1974), No. 1, 85–92

DOI: 10.2140/pjm.1974.55.85

Abstract

A criterion is established for the rationality of series of the form ∑ b_n∕(a₁,⋯,a_n) where a_n,b_n are integers, a_n ≧ 2 and limb_n∕(a_n−1a_n) = 0. This criterion is applied to prove irrationality and rational independence of certain special series of the above type.

Mathematical Subject Classification

Primary: 10F35

Secondary: 10A40

Milestones

Received: 16 April 1974

Published: 1 November 1974