A class of completely monotonic functions involving the gamma and polygamma functions
نویسندگان
چکیده
منابع مشابه
Some Completely Monotonic Functions Involving the Gamma and Polygamma Functions
In this paper, some logarithmically completely monotonic, strongly completely monotonic and completely monotonic functions related to the gamma, digamma and polygamma functions are established. Several inequalities, whose bounds are best possible, are obtained.
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We give an infinite family of functions involving the gamma function whose logarithmic derivatives are completely monotonic. Each such function gives rise to an infinitely divisible probability distribution. Other similar results are also obtained for specific combinations of the gamma and q-gamma functions.
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A class of functions involving the divided differences of the psi function and the polygamma functions and originating from Kershaw’s double inequality are proved to be completely monotonic. As applications of these results, the monotonicity and convexity of a function involving ratio of two gamma functions and originating from establishment of the best upper and lower bounds in Kershaw’s doubl...
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The main object of this work is to give some conditions for a class of functions to be logarithmically completely monotonic. Our result is shown to be an extension of a result which was proven in the recent literature on this subject. c © 2008 Elsevier Ltd. All rights reserved.
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ژورنال
عنوان ژورنال: Cogent Mathematics
سال: 2014
ISSN: 2331-1835
DOI: 10.1080/23311835.2014.982896