Abstract
We shall study some special infinite products obtained by modifying the product expression of the generating function of the Thue-Morse sequence. We first prove that these products are transcendental functions. Then the values of these functions at algebraic points are proved to be transcendental by applying Mahler's method to suitably constructed auxiliary functions. Finally, also irrationality exponents of the values at rational points are considered.
Citation
Peter Bundschuh. Keijo Väänänen. "Arithmetical results on some infinite products." Funct. Approx. Comment. Math. 63 (2) 181 - 188, December 2020. https://doi.org/10.7169/facm/1844
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