Completely monotonic functions associated with the gamma function and its q-analogues
نویسندگان
چکیده
منابع مشابه
COMPLETELY MONOTONIC FUNCTIONS INVOLVING THE GAMMA AND q-GAMMA FUNCTIONS
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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In this paper, the logarithmically complete monotonicity results of the functions [Γ(1 + x)]y/Γ(1 + xy) and Γ(1 + y)[Γ(1 + x)]y/Γ(1 + xy) are established.
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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.
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1986
ISSN: 0022-247X
DOI: 10.1016/0022-247x(86)90042-9