Completely monotonic functions involving the gamma and $q$-gamma functions
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, 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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In the paper, three basic properties of the logarithmically N alternating monotonic functions are established and the monotonicity results of some functions involving the gamma and q-gamma functions, which are obtained in [W. E. Clark and M. E. H. Ismail, Inequalities involving gamma and psi functions, Anal. Appl. (Singap.) 1 (2003), no. 1, 129–140.], are generalized to the logarithmically N -a...
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By a simple approach, two classes of functions involving Euler’s gamma function and originating from certain problems of traffic flow are proved to be logarithmically completely monotonic and a class of functions involving the psi function is showed to be completely monotonic.
متن کاملSome Logarithmically Completely Monotonic Functions Related to the Gamma Function
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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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2005
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-05-08050-0