Hančl, Jaroslav Expression of real numbers with the help of infinite series. (English) Zbl 0701.11005 Acta Arith. 59, No. 2, 97-104 (1991). The paper consists of three theorems which describe conditions for a set \(S\) and for a sequence \(\{a_ n\}^{\infty}_{n=1}\) in order that every real number \(B\in (0,\varepsilon]\) should be expressible in the form \(B=\sum^{\infty}_{n=1}1/a_ n\), where \(a_n\in S\). A criterion for rationality of not too quickly increasing sequences is also presented as a consequence. Reviewer: J.Hančl Cited in 2 ReviewsCited in 6 Documents MSC: 11J72 Irrationality; linear independence over a field 11B34 Representation functions Keywords:representation of real numbers; rationality PDF BibTeX XML Cite \textit{J. Hančl}, Acta Arith. 59, No. 2, 97--104 (1991; Zbl 0701.11005) Full Text: DOI EuDML OpenURL