International Journal of Mathematics and Mathematical Sciences
Volume 2009 (2009), Article ID 865705, 15 pages
doi:10.1155/2009/865705
Engel series and Cohen-Egyptian fraction expansions
Vichian Laohakosol1
, Tuangrat Chaichana2
, Jittinart Rattanamoong2
and Narakorn Rompurk Kanasri4
1Department of Mathematics, Kasetsart University, Bangkok 10900, Thailand
2Department of Mathematics, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand
4Department of Mathematics, Khon Kaen University, Khon Kaen 40002, Thailand
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.