Rational and irrational series consisting of special denominators. (English) Zbl 1023.11036

The author deals with series of the type \(\alpha= \sum_{k=1}^\infty \frac{b_k}{A^{2^k}+ B^{2^k}}\), where \(A\), \(B\) are algebraic numbers, \(1\leq|B|<|A|\), \(A^2\), \(B^2\) are positive integers and \((b_n)\) is a sequence of integers which is connected with the numbers \(A\), \(B\) by certain relations. The author gives some conditions for the rationality of \(\alpha\).


11J72 Irrationality; linear independence over a field
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