77 citations · 2.3k across the 111 of their papers we have counts for
31 papers · 1 filter
Some bounds for the complete elliptic integrals of the first and second kinds
Bai-Ni Guo, Feng Qi
In the article, the complete elliptic integrals of the first and second kinds are bounded by using the power series expansions of some functions, the celebrated Wallis' inequality,…
Complete monotonicity of some functions involving polygamma functions
Feng Qi, Senlin Guo, Bai-Ni Guo
In the present paper, we establish necessary and sufficient conditions for the functions and $α\bigl\lvertψ^{(i)}(x+β)\bigr\lvert-x\bigl\lve…
More supplements to a class of logarithmically completely monotonic functions associated with the gamma function
Senlin Guo, Feng Qi
In this article, a necessary and sufficient condition and a necessary condition are established for a function involving the gamma function to be logarithmically completely monoton…
The function : Ratio's properties
Bai-Ni Guo, Feng Qi
In the paper, after reviewing the history, background, origin, and applications of the functions and , we establish suffic…
Bounds for the ratio of two gamma functions--From Gautschi's and Kershaw's inequalities to completely monotonic functions
Feng Qi
In this expository and survey paper, along one of main lines of bounding the ratio of two gamma functions, we look back and analyse some inequalities, the complete monotonicity of…
Bounds for the ratio of two gamma functions--From Wendel's and related inequalities to logarithmically completely monotonic functions
Feng Qi
In this expository and survey paper, along one of main lines of bounding the ratio of two gamma functions, we look back and analyse some inequalities, several complete monotonicity…
Some properties of extended remainder of Binet's first formula for logarithm of gamma function
Feng Qi, Bai-Ni Guo
In the paper, we extend Binet's first formula for the logarithm of the gamma function and investigate some properties, including inequalities, star-shaped and sub-additive properti…
Uniqueness of nontrivially complete monotonicity for a class of functions involving polygamma functions
Feng Qi, Bai-Ni Guo
For , let on . In the present paper, we prove using two methods that, among all for $m,n…
Concise sharpening and generalizations of Shafer's inequality for the arc sine function
Feng Qi, Bai-Ni Guo
In this paper, by a concise and elementary approach, we sharpen and generalize Shafer's inequality for the arc sine function, and some known results are extended and generalized.
Some logarithmically completely monotonic functions related to the gamma function
Feng Qi, Bai-Ni Guo
In this article, logarithmically complete monotonicity properties of some functions such as , , $\frac{[Γ(x…
A property of logarithmically absolutely monotonic functions and the logarithmically complete monotonicity of a power-exponential function
Feng Qi, Bai-Ni Guo
In the article, a notion "logarithmically absolutely monotonic function" is introduced, an inclusion that a logarithmically absolutely monotonic function is also absolutely monoton…
Necessary and sufficient conditions for a function involving divided differences of the di- and tri-gamma functions to be completely monotonic
Feng Qi, Bai-Ni Guo
In the present paper, necessary and sufficient conditions are established for a function involving divided differences of the digamma and trigamma functions to be completely monoto…
Refinements of lower bounds for polygamma functions
Feng Qi, Bai-Ni Guo
In the paper, some lower bounds for polygamma functions are refined.
Sharp inequalities for polygamma functions
Feng Qi, Bai-Ni Guo
The main aim of this paper is to prove that the double inequality \frac{(k-1)!}{\Bigl\{x+\Bigl[\frac{(k-1)!}{|ψ^{(k)}(1)|}\Bigr]^{1/k}\Bigr\}^k} +\frac{k!}{x^{k+1}}<\bigl|ψ^{(k)}(x…
Monotonicity results and bounds for the inverse hyperbolic sine
Feng Qi, Bai-Ni Guo
In this note, we present monotonicity results of a function involving to the inverse hyperbolic sine. From these, we derive some inequalities for bounding the inverse hyperbolic si…
Logarithmic convexity of Gini means
Feng Qi, Bai-Ni Guo
In the paper, the monotonicity and logarithmic convexity of Gini means and related functions are investigated.
An alternative proof of Elezović-Giordano-Pečarić's theorem
Feng Qi, Bai-Ni Guo
In the present note, an alternative proof is supplied for Theorem~1 in [N. Elezović, C. Giordano and J. Pečarić, \textit{The best bounds in Gautschi's inequality}, Math. Inequal. A…
Some properties of the psi and polygamma functions
Feng Qi, Bai-Ni Guo
In this paper, some monotonicity and concavity results of several functions involving the psi and polygamma functions are proved, and then some known inequalities are extended and…
A note on additivity of polygamma functions
Feng Qi, Bai-Ni Guo
In the note, the functions $\abs{ψ^{(i)}(e^x)}$ for are proved to be sub-additive on and super-additive on , where $θ_i\in(0,1)…
The function : Logarithmic convexity and applications to extended mean values
Feng Qi, Bai-Ni Guo
In the present paper, we first prove the logarithmic convexity of the elementary function , where and . Basing on this, we then provide a simple pro…
Sharpening and generalizations of Shafer's inequality for the arc tangent function
Feng Qi, Bai-Ni Guo
In this paper, we sharpen and generalize Shafer's inequality for the arc tangent function. From this, some known results are refined.
Sharpening and generalizations of Carlson's double inequality for the arc cosine function
Bai-Ni Guo, Feng Qi
In this paper, we sharpen and generalize Carlson's double inequality for the arc cosine function.
Sharp inequalities for the psi function and harmonic numbers
Feng Qi, Bai-Ni Guo
In this paper, two sharp inequalities for bounding the psi function and the harmonic numbers are established respectively, some results in [I. Muqattash and M. Yahdi, \te…
Two new proofs of the complete monotonicity of a function involving the psi function
Feng Qi, Bai-Ni Guo
In the present paper, we give two new proofs for the necessary and sufficient condition such that the function is completely monotonic on .