English

Transcendental Infinite Products Associated with the $\pm 1$ Thue-Morse Sequence

Number Theory 2020-09-07 v1

Abstract

Infinite products associated with the ±1\pm 1 Thue-Morse sequence whose value is rational or algebraic irrational have been studied by several authors. In this short note we prove three new infinite product identities involving π{\pi}, 2\sqrt{2}, and the ±1\pm 1 Thue-Morse sequence, building on a result by Allouche, Riasat, and Shallit. We then use our method to find a new expression for a product appearing within the context of the Flajolet-Martin constant.

Keywords

Cite

@article{arxiv.2009.02025,
  title  = {Transcendental Infinite Products Associated with the $\pm 1$ Thue-Morse Sequence},
  author = {László Tóth},
  journal= {arXiv preprint arXiv:2009.02025},
  year   = {2020}
}