相关论文: The Faa di Bruno formula revisited
In the present note a generalization of Borel-Cantelli Lemma is proposed.
We prove an improved form of an expectation of Polya and discuss several related questions
In this paper, we consider the degenerate poly-Bernoulli polynomials and present new and explicit formulas for computing them in terms of the degenerate Bernoulli polynomials and Stirling numbers of the second kind.
The regularized product of the Fibonacci numbers is evaluated.
Partial ordinary Bell polynomials are used to formulate and prove a version of the Fa\`{a} di Bruno's formula which is convenient for handling nonlinear terms in the differential transformation. Applicability of the result is shown in two…
The purpose of this short note, is to rewrite Morozov's formula for correlation functions over the unitary group, in a much simpler form, involving the computation of a single determinant.
At the first, we revise the Kosinski definition of the sum of ordered fuzzy numbers. The associativity of revised sum is investigated here. In addition, we show that the multiple revised sum of finite sequence of trapezoidal ordered fuzzy…
This paper proposes new derivations of three well-known sorting algorithms, in their functional formulation. The approach we use is based on three main ingredients: first, the algorithms are derived from a simpler algorithm, i.e. the…
In the paper we present some new inversion formulas and two new formulas for Stirling numbers.
A partial fraction decomposition of the Fermi function resulting in a finite sum over simple poles is proposed. This allows for efficient calculations involving the Fermi function in various contexts of electronic structure or electron…
In this paper we give an additive representation of the factorial, which can be proven by a simple quick analytical argument. We also present some generalizations, which are linked, on the one hand to an arithmetical theorem proven by Euler…
We study the explicit formula of Euler numbers and polynomials of higher order
The aim of this research is to provide thirty-two interesting summation formulas for the Kamp\'e de F\'eriet function in general forms, which are given in sixteen theorems. The results are established with the help of the identities in Liu…
The purpose of this note is to present a formulation of a given nonlinear ordinary differential equation into an equivalent system of linear ordinary differential equations. It is evident that the easiness of a such procedure would be able…
This paper presents a family of rapidly convergent summation formulas for various finite sums of analytic functions. These summation formulas are obtained by applying a series acceleration transformation involving Stirling numbers of the…
This paper provides a new approach to derive various arbitrary high order finite difference formulae for the numerical differentiation of analytic functions. In this approach, various first and second order formulae for the numerical…
Using a multivariable Faa di Bruno formula we give conditions on transformations $\tau:[0,1]^m\to\mathcal{X}$ where $\mathcal{X}$ is a closed and bounded subset of $\mathbb{R}^d$ such that $f\circ\tau$ is of bounded variation in the sense…
We describe a simple method that produces automatically closed forms for the coefficients of continued fractions expansions of a large number of special functions. The function is specified by a non-linear differential equation and initial…
In this article a new method of generating sums of like powers is presented.
In the paper, the author finds an explicit formula for computing Bernoulli numbers of the second kind in terms of Stirling numbers of the first kind.