Complete monotonicity of a function involving the gamma function and applications
نویسندگان
چکیده
منابع مشابه
Complete Monotonicity of a Function Involving the Ratio of Gamma Functions and Applications
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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Let a and b be given real numbers with 0 ≤ a < b < a + 1. Then the function θa,b(x) = [Γ(x + b)/Γ(x + a)]1/(b−a) − x is strictly convex and decreasing on (−a,∞) with θa,b(∞) = a+b−1 2 and θa,b(−a) = a, where Γ denotes the Euler’s gamma function.
متن کاملComplete monotonicity involving some ratios of gamma functions
In this paper, by using the properties of an auxiliary function, we mainly present the necessary and sufficient conditions for various ratios constructed by gamma functions to be respectively completely and logarithmically completely monotonic. As consequences, these not only unify and improve certain known results including Qi's and Ismail's conclusions, but also can generate some new inequali...
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ژورنال
عنوان ژورنال: Periodica Mathematica Hungarica
سال: 2014
ISSN: 0031-5303,1588-2829
DOI: 10.1007/s10998-014-0056-x