77 citations · 1.1k across the 47 of their papers we have counts for
39 papers · 1 filter
Refinements of Young's integral inequality via fundamental inequalities and mean value theorems for derivatives
Feng Qi, Wen-Hui Li, Guo-Sheng Wu +1
In the paper, the authors review several refinements of Young's integral inequality via several mean value theorems, such as Lagrange's and Taylor's mean value theorems of Lagrange…
From inequalities involving exponential functions and sums to logarithmically complete monotonicity of ratios of gamma functions
Feng Qi, Bai-Ni Guo
In the paper, the authors review origins, motivations, and generalizations of a series of inequalities involving several exponential functions and sums, establish three new inequal…
A ratio of many gamma functions and its properties with applications
Feng Qi, Wen-Hui Li, Shu-Bin Yu +2
In the paper, the authors establish an inequality involving exponential functions and sums, introduce a ratio of many gamma functions, discuss properties, including monotonicity, l…
Explicit formulae for computing Euler polynomials in terms of Stirling numbers of the second kind
Bai-Ni Guo, Feng Qi
In the paper, the author elementarily unifies and generalizes eight identities involving the functions and their derivatives. By one of these identities,…
Complete monotonicity of functions involving the -trigamma and -tetragamma functions
Feng Qi
Let , , and for stand respectively for the -digamma, -trigamma, and -tetragamma functions. In the paper, the author proves along two diff…
Eight interesting identities involving the exponential function, derivatives, and Stirling numbers of the second kind
Feng Qi
In the paper, the author establishes some identities which show that the functions and the derivatives can be expr…
An inequality involving the gamma and digamma functions
Feng Qi, Bai-Ni Guo
In the paper, we establish an inequality involving the gamma and digamma functions and use it to prove the negativity and monotonicity of a function involving the gamma and digamma…
Sharp bounds for harmonic numbers
Feng Qi, Bai-Ni Guo
In the paper, we first survey some results on inequalities for bounding harmonic numbers or Euler-Mascheroni constant, and then we establish a new sharp double inequality for bound…
A completely monotonic function involving the tri- and tetra-gamma functions
Feng Qi, Bai-Ni Guo
The psi function is defined by and for denote the polygamma functions, where is the gamma function. In this pa…
Two monotonic functions involving gamma function and volume of unit ball
Feng Qi, Bai-Ni Guo
In present paper, we prove the monotonicity of two functions involving the gamma function and relating to the -dimensional volume of the unit ball in $\mat…
A refinement of a double inequality for the gamma function
Feng Qi, Bai-Ni Guo
In the paper, we present a monotonicity result of a function involving the gamma function and the logarithmic function, refine a double inequality for the gamma function, and impro…
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…
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…
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…
A class of completely monotonic functions involving divided differences of the psi and polygamma functions and some applications
Feng Qi, Bai-Ni Guo
A class of functions involving the divided differences of the psi function and the polygamma functions and originating from Kershaw's double inequality are proved to be completely…