Journal of Integer Sequences, Vol. 23 (2020), Article 20.8.2

Transcendental Infinite Products Associated with the ±1 Thue-Morse Sequence

László Tóth
Rue des Tanneurs 7
L-6790 Grevenmacher
Grand Duchy of Luxembourg


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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(Concerned with sequences A010060 A106400.)

Received June 25 2020; revised version received August 28 2020. Published in Journal of Integer Sequences, August 28 2020.

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