Integral representations and properties of some functions involving the logarithmic function
Classical Analysis and ODEs
2016-08-22 v2
Abstract
By using Cauchy integral formula in the theory of complex functions, the authors establish some integral representations for the principal branches of several complex functions involving the logarithmic function, find some properties, such as being operator monotone function, being complete Bernstein function, and being Stieltjes function, for these functions, and verify a conjecture on complete monotonicity of a function involving the logarithmic function.
Cite
@article{arxiv.1305.4083,
title = {Integral representations and properties of some functions involving the logarithmic function},
author = {Feng Qi and Wen-Hui Li},
journal= {arXiv preprint arXiv:1305.4083},
year = {2016}
}
Comments
15 pages