Related papers: Boole's formula as a consequence of Lagrange's Int…
In this paper, we study Grothendieck polynomials from a combinatorial viewpoint. We introduce the factorial Grothendieck polynomials, analogues of the factorial Schur functions and present some of their properties, and use them to produce a…
The basis of this work is a simple, extended corollary of Wilson's theorem. This corollary generates many more quotients than those already generated by Wilson's theorem, and it was of interest to derive how they relate to each other and…
The main purpose of this paper is to construct not only generating functions of the new approach Genocchi type numbers and polynomials but also interpolation function of these numbers and polynomials which are related to a, b, c arbitrary…
We establish an analogue of the Goldbach conjecture for Laurent polynomials with positive integer coefficients.
In this paper we introduce the generalization of Multi Poly-Euler polynomials and we investigate some relationship involving Multi Poly-Euler polynomials. Obtaining a closed formula for generalization of Multi Poly-Euler numbers therefore…
We prove a single sum formula for the linearization coefficients of the Bessel polynomials. In two special cases we show that our formula reduces indeed to Berg and Vignat's formulas in their proof of the positivity results about these…
We construct Lagrange interpolating polynomials for a set of points and values belonging to the algebra of real quaternions $H\simeq R_{0,2}$, or to the real Clifford algebra $R_{0,3}$. In the quaternionic case, the approach by means of…
Stirling's formula is a powerful asymptotic approximation of the factorial function. Many well-known proofs of this formula are grounded in integral calculus. In this paper, we present an alternative proof of Stirling's formula using only…
We provide a proof of Wilson's Theorem and Wolstenholme's Theorem based on a direct approach by Lagrange requiring only basic properties of the primes and the Binomial theorem. The goal is to show how similar the two theorems are by…
It is known that every function with a finite support over a given field can be interpolated by means of the Lagrangian polynomial. The question is if a similar interpolation is possible if one considers a unitary ring or a Boolean algebra…
We present a proof of a conjecture of Goh and Wildberger on the factorization of the spread polynomials. We indicate how the factors can be effectively calculated and exhibit a connection to the factorization of Fibonacci numbers into…
We consider the effective resummation of a Borel sum by its associated factorial series expansion. Our approach provides concrete estimates for the remainder term when truncating this factorial series. We then generalize a theorem of…
Neville's algorithm is known to provide an efficient and numerically stable solution for polynomial interpolations. In this paper, an extension of this algorithm is presented which includes the derivatives of the interpolating polynomial.
In this note we prove that the factorization theorem for dominated polynomials previously proved by the authors is equivalent to an alternative factorization scheme that uses classical linear techniques and a linearization process. However,…
A general theorem on factorization of matrices with polynomial entries is proven and it is used to reduce polynomial Darboux matrices to linear ones. Some new examples of linear Darboux matrices are discussed.
We establish a new generalized Taylor's formula for power fractional derivatives with nonsingular and nonlocal kernels, which includes many known Taylor's formulas in the literature. Moreover, as a consequence, we obtain a general version…
We determine the Rolle function in Lagrange polynomial approximation using a suitable differential equation. We then propose a device for improving the Lagrange approximation by exploiting our knowledge of the Rolle function.
We present generalisations of Wilson's theorem for double factorials, hyperfactorials, subfactorials and superfactorials.
In the present note we prove an asymptotically tight relation between additive and multiplicative complexity of Boolean functions with respect to implementation by circuits over the basis {+,*,1}.
A special Infeld-Hall factorization is given for the Askey-Wilson second order q-difference operator. It is then shown how to deducd a generalization of the corresponding Askey-Wilson polynomials.