Transcendence of a fast converging series of rational numbers (Q2710552)

The author uses a variant of Mahler's method to prove the transcendence of series \(\sum_{n\geq 0} 1/(a^{2^n}+b_n)\) for integers \(a>1\) under no more than an obvious growth restraint on the rationals \(b_n\). His carefully constructed argument, inter alia refining and making explicit suggestions of \textit{J. H. Loxton} and the reviewer [Transcend. Theory Adv. Appl., Proc. Conf., Cambridge 1976, 211-226 (1977; Zbl 0378.10020)], warrants study and further development.