International Journal of Mathematics and Mathematical Sciences
Volume 2009 (2009), Article ID 865705, 15 pages
doi:10.1155/2009/865705
Research Article

Engel Series and Cohen-Egyptian Fraction Expansions

Vichian Laohakosol,1 Tuangrat Chaichana,2,3 Jittinart Rattanamoong,2,3 and Narakorn Rompurk Kanasri4

1Department of Mathematics, Kasetsart University, Bangkok 10900, Thailand
2Department of Mathematics, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand
3The Centre of Excellence in Mathematics, CHE, Si Ayutthaya Road, Bangkok 10400, Thailand
4Department of Mathematics, Khon Kaen University, Khon Kaen 40002, Thailand

Received 11 September 2009; Accepted 2 December 2009

Academic Editor: Stéphane Louboutin

Copyright © 2009 Vichian Laohakosol et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Two kinds of series representations, referred to as the Engel series and the Cohen-Egyptian fraction expansions, of elements in two different fields, namely, the real number and the discrete-valued non-archimedean fields are constructed. Both representations are shown to be identical in all cases except the case of real rational numbers.