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On the logarithm of the derivative operator

Published 30 May 2011 in math.CA, math-ph, and math.MP | (1105.5978v2)

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.

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