On the rationality of Cantor and Ahmes series. (English) Zbl 1018.11037

Tijdeman, R.; Yuan, Pingzhi

Indag. Math., New Ser. 13, No. 3, 407-418 (2002).

The main results of this paper are several criteria for the sums of the Cantor series to be irrational. The authors also prove that if the simple numerators and denominators satisfy some growth conditions then every real number from a certain interval can be expressed in a special form. The proofs are based on interesting tricks. Some remarkable examples are included.

Reviewer: J.Hančl (Ostrava)

MSC:

11J72

Irrationality; linear independence over a field

Keywords:

infinite series; irrational numbers; Cantor series

References:

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