On the logarithm of the derivative operator
Classical Analysis and ODEs
2012-09-12 v2 Mathematical Physics
math.MP
Abstract
We study the properties of the logarithm of the derivative operator and show that its action on a constant is not zero, but yields the sum of the logarithmic function and the Euler-Mascheroni constant. We discuss more general aspects concerning the logarithm of an operator for the study of the properties of the Bessel functions.
Cite
@article{arxiv.1105.5978,
title = {On the logarithm of the derivative operator},
author = {D. Babusci and G. Dattoli},
journal= {arXiv preprint arXiv:1105.5978},
year = {2012}
}
Comments
3 pages, no figures; v2: corrected some typos