Related papers: Representations by ordered Bell and degenerate ord…
In the present paper we derive complicated families of orthogonal polynomials in one variable from scratch using the known ones as building blocks. We recall the basics of operational formalism and introduce the notations we use throughout…
The degenerate exponentials play an important role in recent study on degenerate versions of many special numbers and polynomials, the degenerate gamma function, the degenerate umbral calculus and the degenerate q-umbral calculus. The aim…
This article aims to reinforce the broad applicability of the umbral approach to address complex mathematical challenges and contribute to various scientific and engineering endeavors. The umbral methods are used to reformulate the…
For a bilinear form obtained by adding a Dirac mass to a positive definite moment functional in several variables, explicit formulas of orthogonal polynomials are derived from the orthogonal polynomials associated with the moment…
In this paper we study Appell polynomials by connecting them to random variables. This probabilistic approach yields, e.g., the mean value property which is fundamental in the sense that many other properties can be derived from it. We also…
We consider the problem of inference in higher-order undirected graphical models with binary labels. We formulate this problem as a binary polynomial optimization problem and propose several linear programming relaxations for it. We compare…
In order to verify programs or hybrid systems, one often needs to prove that certain formulas are unsatisfiable. In this paper, we consider conjunctions of polynomial inequalities over the reals. Classical algorithms for deciding these not…
The new method for obtaining a variety of extensions of Hermite polynomials is given. As a first example a family of orthogonal polynomial systems which includes the generalized Hermite polynomials is considered. Apparently, either these…
In this paper, we investigate some properties of several Sheffer sequences of several polynomials arising from umbral calculus. From our investigation, we can derive many interesting identities of several polynomials
Given a finite dimensional representation $M$ of a finite dimensional algebra, two hierarchies of degenerations of $M$ are analyzed in the context of their natural orders: the poset of those degenerations of $M$ which share the top $M/JM$…
Two classifications of second order ODE's cubic with respect to the first order derivative are compared in the first case of intermediate degeneration. The correspondence of vectorial, pseudovectorial, scalar, and pseudoscalar invariants of…
How do we take repeated derivatives of composed multivariate functions? for one-dimensional functions, the common tools consist of the Fa\'a di Bruno formula with Bell polynomials; while there are extensions of the Fa\'a di Bruno formula,…
Departing from a class of infinite series with central binomial coefficients in the numerator and depending on a positive integer parameter, we first extend known identities to all complex parameters. Then we use various methods, including…
We develop a theory of arithmetic Newton polygons of higher order, that provides the factorization of a separable polynomial over a $p$-adic field, together with relevant arithmetic information about the fields generated by the irreducible…
Motivated by the properties of the descent polynomials, which enumerate permutations of $S_n$ with a fixed descent set, we define descent polynomials for labeled rooted trees. We give recursive and explicit formulas for these polynomials…
Exceptional orthogonal Laguerre polynomials can be viewed as an extension of the classical Laguerre polynomials per excluding polynomials of certain order(s) from being eigenfunctions for the corresponding exceptional differential operator.…
In this paper we consider the weighted q-Bernoulli numbers and polynomials which are differnt type of Carlitz's q-Bernoulli numbers and polynomials. From these numbers and polynomials, we derive some interesting formulaes and identities.
We study a class of bivariate deformed Hermite polynomials and some of their properties using classical analytic techniques and the Wigner map. We also prove the positivity of certain determinants formed by the deformed polynomials. Along…
In this paper we investigate some interesting formulae of q-Euler numbers and polynomials related to the modified q-Bernstein polynomials.
The purpose of this work is to analyse a family of mutually orthogonal polynomials on the unit ball with respect to an inner product which includes an additional term on the sphere. First, we will get connection formulas relating classical…