Some completely monotonic functions related to the psi function
نویسندگان
چکیده
منابع مشابه
Some Completely Monotonic Functions Related to the Psi Function
Complete monotonicity properties of some functions involving the psi function are studied and some known results are extended and generalized. Moreover, a necessary and sufficient conditions for some functions to be completely monotonic are presented and proved. Mathematics subject classification (2010): 33B15, 26D15.
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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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A function f : (0,∞) → R is said to be completely monotonic if (−1)nf (n)(x) ≥ 0 for all x > 0 and n = 0, 1, 2, .... In this paper we present several new classes of completely monotonic functions. Our functions have in common that they are defined in terms of the classical gamma, digamma, and polygamma functions. Moreover, we apply one of our monotonicity theorems to prove a new inequality for ...
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ژورنال
عنوان ژورنال: Mathematical Inequalities & Applications
سال: 2011
ISSN: 1331-4343
DOI: 10.7153/mia-14-57