A certain function class related to the class of logarithmically completely monotonic functions
نویسندگان
چکیده
منابع مشابه
A class of logarithmically completely monotonic functions
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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converges for x ∈ [0,∞). This tells us that f ∈ C[[0,∞)] if and only if it is a Laplace transform of the measure α. There have been a lot of literature about the completely monotonic functions, for examples, [3, 4, 5, 22, 25, 32, 34, 35, 39, 40, 42, 58, 60, 61, 62, 63, 66] and references therein. Recall also [6, 43, 47] that a positive function f is said to be logarithmically completely monoton...
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In this article, a necessary and sufficient condition and a necessary condition are established for a function involving the gamma function to be logarithmically completely monotonic on (0,∞). As applications of the necessary and sufficient condition, some inequalities for bounding the psi and polygamma functions and the ratio of two gamma functions are derived. This is a continuator of the pap...
متن کاملA Class of Logarithmically Completely Monotonic Functions Associated with the Gamma Function
In this article, a necessary condition, several sufficient conditions and a sufficient and necessary condition for a class of functions involving the gamma function to be logarithmically completely monotonic are established, and then some known results are extended.
متن کاملA Class of Logarithmically Completely Monotonic Functions Associated with a Gamma Function
For extension of these functions to complex variables and for basic properties, see 1 . These functions play central roles in the theory of special functions and have lots of extensive applications in many branches, for example, statistics, physics, engineering, and other mathematical sciences. Over the past half century monotonicity properties of these functions have attracted the attention of...
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ژورنال
عنوان ژورنال: Mathematical and Computer Modelling
سال: 2009
ISSN: 0895-7177
DOI: 10.1016/j.mcm.2009.01.002