77 citations · 2.3k across the 111 of their papers we have counts for
113 papers
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…
Monotonicity and absolute convexity of two functions involving Riemann zeta function
Bai-Ni Guo, Feng Qi
Let be a constant, let be an integer, and let denote the Euler gamma function. With the aid of the integral representation for the Riemann zeta function …
Taylor's series expansions for real powers of functions containing squares of inverse (hyperbolic) cosine functions, explicit formulas for special partial Bell polynomials, and series representations for powers of circular constant
Feng Qi
In the paper, by virtue of expansions of two finite products of finitely many square sums, with the aid of series expansions of composite functions of (hyperbolic) sine and cosine…
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…
A power series expansion of the Wilf function
Feng Qi
In this work, the author employs the Faà di Bruno formula, identities for the partial Bell polynomials, two combinatorial identities, and the (logarithmically) complete monotonicit…
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.…
Several combinatorial identities derived from series expansions of powers of arcsine
Feng Qi, Chao-Ping Chen, Dongkyu Lim
In the paper, with the aid of the series expansions of the square or cubic of the arcsine function, the authors establish several possibly new combinatorial identities containing t…
Maclaurin's series expansions for positive integer powers of inverse (hyperbolic) sine and related functions, specific values of partial Bell polynomials, and two applications
Bai-Ni Guo, Dongkyu Lim, Feng Qi
In the paper, the authors establish Maclaurin's series expansions and series identities for positive integer powers of the inverse sine function, for positive integer powers of the…
An analytic generalization of the Catalan numbers and its integral representation
Wen-Hui Li, Jian Cao, Da-Wei Niu +2
In the paper, the authors analytically generalize the Catalan numbers in combinatorial number theory, establish an integral representation of the analytic generalization of the Cat…
A determinantal expression and a recursive relation of the Delannoy numbers
Feng Qi
In the paper, by a general and fundamental, but non-extensively circulated, formula for derivatives of a ratio of two differentiable functions and by a recursive relation of the He…
A double inequality for completely monotonic degree of a remainder for an asymptotic expansion of the trigamma function
Feng Qi
In the paper, the author presents a double inequality for completely monotonic degree of a remainder for an asymptotic expansion of the trigamma function. This result partially con…
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…
Extended Weyl fractional integrals and their inequalities
Praveen Agarwal, Mohamed Jleli, Feng Qi
In the paper, the authors establish some interesting identities and inequalities involving the extended Weyl type fractional integrals.
Two closed forms for the Bernoulli polynomials
Feng Qi, Robin J. Chapman
In the paper, the authors find two closed forms involving the Stirling numbers of the second kind and in terms of a determinant of combinatorial numbers for the Bernoulli polynomia…
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…
A new explicit formula for Bernoulli and Genocchi numbers in terms of Stirling numbers
Bai-Ni Guo, Feng Qi
In the paper, the authors review some explicit formulas and establish a new explicit formula for Bernoulli and Genocchi numbers in terms of Stirling numbers of the second kind.
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+…