77 citations · 2.3k across the 111 of their papers we have counts for
14 papers · 1 filter
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…
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…
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…
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…
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.
Diagonal recurrence relations, inequalities, and monotonicity related to Stirling numbers
Feng Qi
In the paper, the author derives several "diagonal" recurrence relations, constructs some inequalities, finds monotonicity, and poses a conjecture related to Stirling numbers of th…
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 computing Bell numbers in terms of Lah and Stirling numbers
Feng Qi
In the paper, the author finds an explicit formula for computing Bell numbers in terms of Lah numbers and Stirling numbers of the second kind.
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 note on the modified q-Genocchi numbers and polynomials with weight (α,β) and their interpolation function at negative integers
Serkan Araci, Mehmet Açikgöz, Feng Qi +1
The purpose of this paper concerns to establish modified q-Genocchi numbers and polynomials with weight (α,β). In this paper we investigate special generalized q-Genocchi polynomia…