Jacobi continued fraction and Hankel determinants of the Thue-Morse sequence

Abstract

We study the Jacobi continued fraction and the Hankel determinants of the Thue-Morse sequence and obtain several interesting properties. In particular, a formal power series ϕ(x) is being discovered, having the property that the Hankel transforms of ϕ(x) and of ϕ(x²) are identical.

Mathematics Subject Classification (2010): 05A15, 05A19, 11A55, 11B37, 11B50, 11B85, 11C20, 15A15.

Keywords: Hankel determinant, Hankel transform, binomial transform, Jacobi continued fraction, Thue-Morse sequence, Gros sequence