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

Abstract

Infinite products associated with the $\pm 1$ 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 $\pi$, $\sqrt{2}$, and the $\pm 1$ 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.

References in corpus (1)

• Infinite products with strongly $B$-multiplicative exponents