Complete monotonicity and inequalities related to generalized k-gamma and k-polygamma functions
نویسندگان
چکیده
منابع مشابه
Complete 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) ̨
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In particular they proved that for x > 0 and α = 0 the function [Γ(1 + 1/x)]x decreases with x, while when α=1 the function x[Γ(1+1/x)]x increases.Moreover they also showed that the values α= 0 and α= 1, in the properties mentioned above, cannot be improved if x ∈ (0,+∞). In this paper we continue the investigation on the monotonicity properties for the gamma function proving, in Section 2, the...
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ژورنال
عنوان ژورنال: Journal of Inequalities and Applications
سال: 2020
ISSN: 1029-242X
DOI: 10.1186/s13660-020-2287-0