77 citations · 1.1k across the 47 of their papers we have counts for
48 papers
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 …
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…
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…
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.
An explicit formula for Bell numbers in terms of Stirling numbers and hypergeometric functions
Feng Qi
In the paper, the author finds an explicit formula for computing Bell numbers in terms of Kummer confluent hypergeometric functions and Stirling numbers of the second kind.
An explicit formula for Bernoulli polynomials in terms of -Stirling numbers of the second kind
Bai-Ni Guo, István Mező, Feng Qi
In the paper, the authors establish an explicit formula for computing Bernoulli polynomials at non-negative integer points in terms of -Stirling numbers of the second kind.
Some integral representations and properties of Lah numbers
Bai-Ni Guo, Feng Qi
In the paper, the authors find some integral representations and discover some properties of Lah numbers.
Six proofs for an identity of the Lah numbers
Bai-Ni Guo, Feng Qi
In the paper, utilizing respectively the induction, a generating function of the Lah numbers, the Chu-Vandermonde summation formula, an inversion formula, the Gauss hypergeometric…
An explicit formula for Bernoulli numbers in terms of Stirling numbers of the second kind
Feng Qi
In the note, the author discovers an explicit formula for computing Bernoulli numbers in terms of Stirling numbers of the second kind.
Alternative proofs of a formula for Bernoulli numbers in terms of Stirling numbers
Bai-Ni Guo, Feng Qi
In the paper, the authors provide four alternative proofs of an explicit formula for computing Bernoulli numbers in terms of Stirling numbers of the second kind.
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…