Transcendental Infinite Products Associated with the 1 Thue-Morse Sequence
Abstract
Infinite products associated with the 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, 2, and the 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.
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