Complete monotonicity of a function involving the divided difference of digamma functions
نویسندگان
چکیده
منابع مشابه
Complete Monotonicities of Functions Involving the Gamma and Digamma Functions
In the article, the completely monotonic results of the functions [Γ(x+ 1)]1/x, [Γ(x+α+1)]1/(x+α) [Γ(x+1)]1/x , [Γ(x+1)]1/x (x+1)α and [Γ(x+1)]1/x xα in x ∈ (−1,∞) for α ∈ R are obtained. In the final, three open problems are posed.
متن کاملComplete monotonicity of some functions involving polygamma functions
In the present paper, we establish necessary and sufficient conditions for the functions x ̨ ̨ψ(i)(x + β) ̨ ̨ and α ̨ ̨ψ(i)(x + β) ̨ ̨ − x ̨ ̨ψ(i+1)(x + β) ̨
متن کاملComplete 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...
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...
متن کاملA Completely Monotonic Function Involving the Divided Difference of the Psi Function and an Equivalent Inequality Involving Sums
In this paper, a function involving the divided difference of the psi function is proved to be completely monotonic, a class of inequalities involving sums is found, and an equivalent relation between complete monotonicity and one of the class of inequalities is established. 2000 Mathematics subject classification: primary 33B15, 26D15; secondary 26A48, 26A51.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Science China Mathematics
سال: 2013
ISSN: 1674-7283,1869-1862
DOI: 10.1007/s11425-012-4562-0