Journal article
Irrationality of certain infinite series
Publication Details
Authors: | Koepf, W.; Schmersau, D. |
Publication year: | 2010 |
Journal: | Analysis |
Pages range : | 27-34 |
Volume number: | 30 |
URN / URL: |
Abstract
In this paper a new direct proof for the irrationality of Euler's number e =sum(1/k!,k=0..infinity) is presented. Furthermore, formulas for the base b digits are given which, however, are not computablyeffective. Finally we generalize our method and give a simple criterium for some fastconverging series representing irrational numbers.
In this paper a new direct proof for the irrationality of Euler's number e =sum(1/k!,k=0..infinity) is presented. Furthermore, formulas for the base b digits are given which, however, are not computablyeffective. Finally we generalize our method and give a simple criterium for some fastconverging series representing irrational numbers.
