77 citations · 2.3k across the 111 of their papers we have counts for
28 papers · 1 filter
Asymptotic formulas and inequalities for gamma function in terms of tri-gamma function
Cristinel Mortici, Feng Qi
In the paper, the authors establish some asymptotic formulas and double inequalities for the factorial and the gamma function in terms of the tri-gamma function .
Some best approximation formulas and inequalities for Wallis ratio
Feng Qi, Cristinel Mortici
In the paper, the authors establish some best approximation formulas and inequalities for Wallis ratio. These formulas and inequalities improve an approximation formula and a doubl…
A unified proof of inequalities and some new inequalities involving Neuman-Sándor mean
Wen-Hui Li, Feng Qi
In the paper, by finding linear relations of differences between some means, the authors supply a unified proof of some double inequalities for bounding Neuman-Sándor means in term…
Extended fermionic -adic integrals on
Feng Qi, Serkan Araci, Mehmet Acikgoz
In the paper, using the extended fermionic -adic integral on , the authors find some applications of the umbral calculus. From these applications, the authors deri…
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,…
Diagonal recurrence relations for the Stirling numbers of the first kind
Feng Qi
In the paper, the author presents diagonal recurrence relations for the Stirling numbers of the first kind. As by-products, the author also recovers three explicit formulas for spe…
Some integral inequalities of Hermite-Hadamard type for functions whose derivatives of -th order are -convex
Feng Qi, Muhammad Amer Latif, Wen-Hui Li +1
In the paper, the authors find some new integral inequalities of Hermite-Hadamard type for functions whose derivatives of the -th order are -convex and deduce some known…
A completely monotonic function involving the gamma and tri-gamma functions
Feng Qi
In the paper the author provides necessary and sufficient conditions on for the function and i…
Integral inequalities of Hermite-Hadamard type for -GA-convex functions
Ai-Ping Ji, Tian-Yu Zhang, Feng Qi
In the paper, the authors introduce a notion "-GA-convex functions" and establish some integral inequalities of Hermite-Hadamard type for -GA-convex functions.
Hermite-Hadamard type integral inequalities for functions whose first derivatives are of convexity
Feng Qi, Tian-Yu Zhang, Bo-Yan Xi
In the paper, the authors establish some new Hermite-Hadamard type inequalities for functions whose first derivatives are of convexity and apply these inequalities to construct ine…
Integral representations and properties of some functions involving the logarithmic function
Feng Qi, Wen-Hui Li
By using Cauchy integral formula in the theory of complex functions, the authors establish some integral representations for the principal branches of several complex functions inv…
Integral representations of the weighted geometric mean and the logarithmic mean
Feng Qi, Xiao-Jing Zhang, Wen-Hui Li
In the paper, the authors show that the weighted geometric mean and the logarithmic mean are Bernstein functions and establish integral representations of these means by Cauchy's i…
The best bounds for Toader mean in terms of the centroidal and arithmetic means
Yun Hua, Feng Qi
In the paper, the authors discover the best constants , , , and for the double inequalities $$ α_{1}\bar{C}(a,b)+(1-α_{1}) A(a,b)< T(a,b) <β_{1} \bar{C…
Complete monotonicity of a difference between the exponential and trigamma functions
Feng Qi, Xiao-Jing Zhang
In the paper, by directly verifying an inequality which gives a lower bound for the first order modified Bessel function of the first kind, the authors supply a new proof for the c…
A logarithmically completely monotonic function involving the ratio of gamma functions
Feng Qi, Wen-Hui Li
In the paper, the authors concisely survey and review some functions involving the gamma function and its various ratios, simply state their logarithmically complete monotonicity a…
Properties of modified Bessel functions and completely monotonic degrees of differences between exponential and trigamma functions
Feng Qi
In the paper, the author establishes inequalities, monotonicity, convexity, and unimodality for functions concerning the modified Bessel functions of the first kind and compute the…
An integral representation and properties of Bernoulli numbers of the second kind
Feng Qi
In the paper, the author establishes an integral representation and properties of Bernoulli numbers of the second kind and reveals that the generating function of Bernoulli numbers…
The geometric mean is a Bernstein function
Feng Qi, Xiao-Jing Zhang, Wen-Hui Li
In the paper, the authors establish, by using Cauchy integral formula in the theory of complex functions, an integral representation for the geometric mean of positive numbers.…
Explicit formulas for computing Bernoulli numbers of the second kind and Stirling numbers of the first kind
Feng Qi
In the paper, by establishing a new and explicit formula for computing the -th derivative of the reciprocal of the logarithmic function, the author presents new and explicit for…
A new proof of the geometric-arithmetic mean inequality by Cauchy's integral formula
Feng Qi, Xiao-Jing Zhang, Wen-Hui Li
Let for be a given sequence of positive numbers. In the paper, the authors establish, by using Cauchy's integral formula in the theory of co…
Some Bernstein functions and integral representations concerning harmonic and geometric means
Feng Qi, Xiao-Jing Zhang, Wen-Hui Li
It is general knowledge that the harmonic mean and that the geometric mean , where and are two positive numbers. In the…
Some inequalities for complete elliptic integrals
Li Yin, Feng Qi
In the paper, by using Lupaş integral inequality, the authors find some new inequalities for the complete elliptic integrals of the first and second kinds. These results improve so…
Sharp bounds in terms of the power of the contra-harmonic mean for Neuman-Sandor mean
Wei-Dong Jiang, Feng Qi
In the paper, the authors obtain sharp bounds in terms of the power of the contra-harmonic mean for Neuman-Sándor mean.
Sharp bounds for Neuman-Sándor's mean in terms of the root-mean-square
Wei-Dong Jiang, Feng Qi
In the paper, the authors find sharp bounds for Neuman-Sándor's mean in terms of the root-mean-square.