Letting (t n ) denote the Thue-Morse sequence with values 0, 1, we note that the Woods-Robbins product n≥0 2n + 1 2n + 2 (−1) tn = 2 −1/2 involves a rational function in n and the ±1 Thue-Morse sequence ((−1) tn ) n≥0 . The purpose of this paper is twofold. On the one hand, we try to find other rational functions for which similar infinite products involving the ±1 Thue-Morse sequence have an expression in terms of known constants. On the other hand, we also try to find (possibly different) rational functions R for which the infinite product R(n) tn also has an expression in terms of known constants.

Let (u n ) n≥0 denote the Thue-Morse sequence with values ±1. The Woods-Robbins identity below and several of its generalisations are well-known in the literature ∞ ∏ n=0 arXiv:1709.04104v2 [math.NT]

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