Logarithmically complete monotonicity of a power-exponential function involving the logarithmic and psi functions
نویسندگان
چکیده
منابع مشابه
A Property of Logarithmically Absolutely Monotonic Functions and the Logarithmically Complete Monotonicity of a Power-exponential Function
In the article, a notion “logarithmically absolutely monotonic function” is introduced, an inclusion that a logarithmically absolutely monotonic function is also absolutely monotonic is revealed, the logarithmically complete monotonicity and the logarithmically absolute monotonicity of the function ` 1+ α x ́x+β are proved, where α and β are given real parameters, a new proof for the inclusion t...
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Let L(x) := x − Γ(x+t) Γ(x+s) xs−t+1, where Γ(x) is Euler’s gamma function. We determine conditions for the numbers s, t so that the function Φ(x) := − Γ(x+t) xt−s−1 L′′(x) is strongly completely monotonic on (0, ∞). Through this result we obtain some inequalities involving the ratio of gamma functions and provide some applications in the context of trigonometric sum estimation. We also give se...
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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.
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In the paper, necessary and sufficient conditions are presented for a function involving a ratio of gamma functions to be logarithmically completely monotonic. This extends and generalizes the main result of Guo and Qi [Taiwanese J. Math. 7 (2003), no. 2, 239–247] and others. As applications, several inequalities involving the volume of the unit ball in R are derived, which refine, generalize a...
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ژورنال
عنوان ژورنال: Global Journal of Mathematical Analysis
سال: 2015
ISSN: 2307-9002
DOI: 10.14419/gjma.v3i2.4605