77 citations · 2.3k across the 111 of their papers we have counts for
89 papers · 1 filter
Several series expansions for real powers and several formulas for partial Bell polynomials of sinc and sinhc functions in terms of central factorial and Stirling numbers of second kind
Feng Qi, Peter Taylor
In the paper, with the aid of the Faà di Bruno formula, in terms of central factorial numbers of the second kind, and with the terminology of the Stirling numbers of the second kin…
Parametric kinds of generalized Apostol-Bernoulli polynomials and their properties
Zeynep Özat, Bayram Çekim, Can Kızılateş +1
The purpose of this paper is to define generalized Apostol--Bernoulli polynomials with including a new cosine and sine parametric type of generating function using the quasi-monomi…
Logarithmic complete monotonicity of a matrix-parametrized analogue of the multinomial distribution
Frédéric Ouimet, Feng Qi
In the paper, the authors introduce a matrix-parametrized generalization of the multinomial probability mass function that involves a ratio of several multivariate gamma functions.…
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…
Partial solutions to several conjectures on completely monotonic degrees for remainders in asymptotic expansions of the digamma function
Feng Qi, Mansour Mahmoud
Motivated by several conjectures posed in the paper "F. Qi and A.-Q. Liu, Completely monotonic degrees for a difference between the logarithmic and psi functions, J. Comput. Appl.…
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…
Some inequalities for the trigamma function in terms of the digamma function
Feng Qi, Cristinel Mortici
In the paper, the authors establish three kinds of double inequalities for the trigamma function in terms of the exponential function to powers of the digamma function. These newly…
Inequalities of Hermite-Hadamard type for extended -convex functions and applications to means
Bo-Yan Xi, Feng Qi
In the paper, the authors introduce a new concept "extended -convex functions", establish some new integral inequalities of Hermite-Hadamard type for this kind of functions, and…
Explicit expressions for a family of Bell polynomials and derivatives of some functions
Feng Qi, Miao-Miao Zheng
In the paper, the authors first inductively establish explicit formulas for derivatives of the arc sine function, then derive from these explicit formulas explicit expressions for…
Integral representations and complete monotonicity related to the remainder of Burnside's formula for the gamma function
Feng Qi
In the paper, the authors establish integral representations of some functions related to the remainder of Burnside's formula for the gamma function and find the (logarithmically)…
A double inequality for bounding Toader mean by the centroidal mean
Yun Hua, Feng Qi
In the paper, the authors find the best numbers and such that for all…
Bounds for the combination of Toader mean and the arithmetic mean in terms of the contraharmonic mean
Wei-Dong Jiang, Feng Qi
In the paper, the authors find the greatest value and the least value such that the double inequality \begin{multline*} C(λa+(1-λ)b,λb+(1-λ)a)<αA(a,b)+(1-α)T(a,b)\\ < C(μa+…
An integral representation, complete monotonicity, and inequalities of Cauchy numbers of the second kind
Feng Qi
In the paper, the author establishes an integral representation for Cauchy numbers of the second kind, finds the complete monotonicity, minimality, and logarithmic convexity of Cau…
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…
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…