On the continued fraction expansion of certain Engel series
Abstract
An Engel series is a sum of the reciprocals of an increasing sequence of positive integers, which is such that each term is divisible by the previous one. Here we consider a particular class of Engel series, for which each term of the sequence is divisible by the square of the preceding one, and find an explicit expression for the continued fraction expansion of the sum of a generic series of this kind. As a special case, this includes certain series whose continued fraction expansion was found by Shallit. A family of examples generated by nonlinear recurrences with the Laurent property is considered in detail, along with some associated transcendental numbers.
Keywords
Cite
@article{arxiv.1508.07438,
title = {On the continued fraction expansion of certain Engel series},
author = {Andrew N. W. Hone},
journal= {arXiv preprint arXiv:1508.07438},
year = {2015}
}
Comments
Compared with v1, paper rewritten to take results of Kempner and Shallit into account