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arXiv · 2009.02025

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

László Tóth
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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 $π$, $\sqrt{2}$, 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.

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László Tóth. 2020-09-04. Transcendental Infinite Products Associated with the $\pm 1$ Thue-Morse Sequence. https://arxiv.org/abs/2009.02025

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