On the logarithm of the derivative operator
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 EulerMascheroni constant. We discuss more general aspects concerning the logarithm of an operator for the study of the properties of the Bessel functions.
 Publication:

arXiv eprints
 Pub Date:
 May 2011
 arXiv:
 arXiv:1105.5978
 Bibcode:
 2011arXiv1105.5978B
 Keywords:

 Mathematics  Classical Analysis and ODEs;
 Mathematical Physics;
 33;
 26A33
 EPrint:
 3 pages, no figures