Related papers: Hermite Calculus
This paper is now part of the new paper "Series with Hermite polynomials and applications" arXiv:1710.00687.
Every real hyperbolic form in three variables can be realized as the determinant of a linear net of Hermitian matrices containing a positive definite matrix. Such representations are an algebraic certificate for the hyperbolicity of the…
The present survey results from the will to reconcile two approaches to quantum probabilities: one rather physical and coming directly from quantum mechanics, the other more algebraic. The second leading idea is to provide a unified picture…
In this paper, we consider the problem of representing any polynomial in terms of the degenerate Bernoulli polynomials and more generally of the higher-order degenerate Bernoulli polynomials. We derive explicit formulas with the help of…
We use the Legendre polynomials and the Hermite polynomials as two examples to illustrate a simple and systematic technique on deriving asymptotic formulas for orthogonal polynomials via recurrence relations. Another application of this…
A class of generalized complex polynomials of Hermite type, suggested by a special magnetic Schrodinger operator, is introduced and some related basic properties are discussed.
The umbral approach provides methods for comprehending and redefining special functions. This approach is employed efficiently in order to uncover intricacies and introduce new families of special functions. In this article, the umbral…
In this paper, by using the orthogonality type as defined in the umbral calculus, we derive explicit formula for several well known polynomials as a linear combination of the Apostol-Euler polynomials.
In this paper, we investigate the power of nearly purely operational techniques in the study of umbral calculus. We present a concise reconstruction of the theory based on a systematic use of linear operators, with particular attention to…
Generalizations of the Hermite polynomials to many variables and/or to the complex domain have been located in mathematical and physical literature for some decades. Polynomials traditionally called complex Hermite ones are mostly…
We define a new Hurwitz problem which is essentially a small core of the simple Hurwitz problem. The corresponding Hurwitz numbers have simpler formulae, satisfy effective recursion relations and determine the simple Hurwitz numbers. We…
We determine a new technique which allows the computation of the arithmetical rank of certain monomial ideals.
In this paper, we give some interesting identities of higher-order Bernoulli, Frobenius-Euler and Euler polynomials arising from umbral calculus. From our method of this paper, we can derive many interesting identities of special…
In this paper we develop a new technique to compute the Betti table of a monomial ideal. We present a prototype implementation of the resulting algorithm and we perform numerical experiments suggesting a very promising efficiency. On the…
The aim of this paper is to develop foundations of umbral calculus on the space $\mathcal D'$ of distributions on $\mathbb R^d$, which leads to a general theory of Sheffer polynomial sequences on $\mathcal D'$. We define a sequence of monic…
We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such…
In this note we give a theoretical support by means of quotient polynomial rings for the computation formulas of the dimension of abelian codes.
We investigate a type of Hermite orthogonal polynomials on $r$ lines in the plane which have a common point at the origin and endpoints at the $r$ roots of unity and we show that their related Hermite functions are eigenfunctions of a…
We provide a systematic study of sesquilinear hermitian forms and a new proof of the calculus of some exponential sums defined with quadratic hermitian forms. The computation of the number of solutions of equations such as Tr(f(x)+v.x)=0 or…
A Las Vegas randomized algorithm is given to compute the Hermite normal form of a nonsingular integer matrix $A$ of dimension $n$. The algorithm uses quadratic integer multiplication and cubic matrix multiplication and has running time…