Complete monotonicity of some functions involving k-digamma function with application
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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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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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: Journal of Mathematical Inequalities
سال: 2021
ISSN: 1846-579X
DOI: 10.7153/jmi-2021-15-17