2020/06/08 by Li, Shuo
#Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2006.04909
In this article we introduce a new approach to compute infinite products defined by automatic sequences involving the Thue-Morse sequence. As examples, for any positive integers q and r such that 0 ≤ r ≤ q-1, we find infinitely many couples of rational functions R(x) and S(n) such that ∏n=0∞R(n)(1+an)/(2)S(n)(1-an)/(2)=2cos((2r+1)/(2q)π), where (an)n ∈ N is the Thue-Morse sequence beginning with a0=1,a1= -1.