Simple continued fractions for the Fredholm numbers

AbstractLet {ai} with a1 ≥ 2 be an infinite bounded sequence of positive integers, and d1 = 1, di = ±1 for i = 2, 3,…. Let {Qi} be another sequence defined by the recursion Q1 = 1, Qi = ai−1Qi−1k for i = 2, 3,…, where k ≥ 2 an integer. Put Ck(a) = Σi = 1∞diQi−1. In this paper we shall determine the simple continued fraction expansion for the real numbers Ck(a)