2017/09/13 by Riasat, Samin
#11A63 #11B83 #11B85 #68R15 #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.1709.04104
Let (un)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^∞((2n+1)/(2n+2))un=(1)/(√ 2). No other such product involving a rational function in n and the sequence un seems to be known in closed form. To understand these products in detail we study the function f(b,c)=∏n=1^∞((n+b)/(n+c))un. We prove some analytical properties of f. We also obtain some new identities similar to the Woods-Robbins product.