D. Babusci, G. Dattoli
Published 2011-05-30, updated 2012-09-11Version 2
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.
Comments: 3 pages, no figures; v2: corrected some typos
Integral representations and properties of some functions involving the logarithmic function
On the $n$-th derivative and the fractional integration of Bessel functions with respect to the order
On evaluation of integrals involving Bessel functions
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