Values of arbitrary Mahler Mq-functions at nonzero algebraic points obey a Liouville-type inequality and therefore cannot be Liouville numbers or U-numbers.
Zorin, Algebraic independence and normality of the values of Mahle r’s functions , preprint 2013, arXiv:1309.0105 [math.NT]
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A Liouville-Type Inequality for Values of Mahler M-Functions
Values of arbitrary Mahler Mq-functions at nonzero algebraic points obey a Liouville-type inequality and therefore cannot be Liouville numbers or U-numbers.