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Mathematics > Classical Analysis and ODEs

arXiv:0709.1788 (math)
[Submitted on 12 Sep 2007]

Title:Leonhard Euler and a q-analogue of the logarithm

Authors:Erik Koelink, Walter Van Assche
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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.
Comments: 13 pages, to appear in Proc. AMS
Subjects: Classical Analysis and ODEs (math.CA); History and Overview (math.HO)
Cite as: arXiv:0709.1788 [math.CA]
  (or arXiv:0709.1788v1 [math.CA] for this version)
  https://doi.org/10.48550/arXiv.0709.1788
Journal reference: Proc AMS 137 (2009), no. 5, 1663-1676
Related DOI: https://doi.org/10.1090/S0002-9939-08-09374-X

Submission history

From: Erik Koelink [view email]
[v1] Wed, 12 Sep 2007 10:15:43 UTC (13 KB)
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