Leonhard Euler and a q-analogue of the logarithm
Classical Analysis and ODEs
2014-04-17 v1 History and Overview
Abstract
We study a q-logarithm which was introduced by Euler and give some of its properties. This q-logarithm did not get much attention in the recent literature. We derive basic properties, some of which were already given by Euler in a 1751-paper and 1734-letter to Daniel Bernoulli. The corresponding q-analogue of the dilogarithm is introduced. The relation to the values at 1 and 2 of a q-analogue of the zeta function is given. We briefly describe some other q-logarithms that have appeared in the recent literature.
Keywords
Cite
@article{arxiv.0709.1788,
title = {Leonhard Euler and a q-analogue of the logarithm},
author = {Erik Koelink and Walter Van Assche},
journal= {arXiv preprint arXiv:0709.1788},
year = {2014}
}
Comments
13 pages, to appear in Proc. AMS