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arXiv · 0709.1788

Leonhard Euler and a q-analogue of the logarithm

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.

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Erik Koelink, Walter Van Assche. 2007-09-12. Leonhard Euler and a q-analogue of the logarithm. https://doi.org/10.1090/s0002-9939-08-09374-x

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