Related papers: Matrix valued Laguerre polynomials
In this article, the 2-iterated Sheffer polynomials are introduced by means of generating function and operational representation. Using the theory of Riordan arrays and relations between the Sheffer sequences and Riordan arrays, a…
Matrix element reweighting is a powerful experimental technique widely employed to maximize the amount of information that can be extracted from a collider data set. We present a procedure that allows to automatically evaluate the weights…
We discuss several constructions of swap polynomials, that is 2--tensor valued matrix polynomials which are multiples of the swap or switch operator.
The aim of this paper is to present the construction of exceptional Laguerre polynomials in a systematic way, and to provide new asymptotic results on the location of the zeros. To describe the exceptional Laguerre polynomials we associate…
Many mathematicians have been studying various degenerate versions of special polynomials and numbers in some arithmetic and combinatorial aspects. Our main focus here is a new type of degenerate poly-Euler polynomials and numbers. This…
The aim of this paper is to study differential properties of orthogonal polynomials with respect to a discrete Laguerre-Sobolev bilinear form with mass point at zero. In particular we construct the orthogonal polynomials using certain…
Systems subjected to holonomic constraints follow quite complicated dynamics that could not be described easily with Hamiltonian or Lagrangian dynamics. The influence of holonomic constraints in equations of motions is taken into account by…
In this paper we present methods for the synthesis of polynomial invariants for probabilistic transition systems. Our approach is based on martingale theory. We construct invariants in the form of polynomials over program variables, which…
By means of a symbolic method, in this paper we introduce a new family of multivariate polynomials such that multivariate L\'evy processes can be dealt with as they were martingales. In the univariate case, this family of polynomials is…
In this article, a new approach based on linear algebra is adopted to study a hybrid Sheffer polynomial sequences. The recurrence relations and differential equation for these polynomials are derived by using the properties and…
We present a new algorithm for the computation of the irreducible factors of degree at most $d$, with multiplicity, of multivariate lacunary polynomials over fields of characteristic zero. The algorithm reduces this computation to the…
An algebraic interpretation of matrix-valued orthogonal polynomials (MVOPs) is provided. The construction is based on representations of a ($q$-deformed) Lie algebra $\mathfrak{g}$ into the algebra $\operatorname{End}_{M_n(\mathbb{C})}(M)$…
In Part 1 we study the spherical functions on compact symmetric pairs of arbitrary rank under a suitable multiplicity freeness assumption and additional conditions on the branching rules. The spherical functions are taking values in the…
Admissable weight is an important tool for studying spectral invariance in operator algebra. Common admissable weights include polynomial weights and sub exponential weights. This article mainly provides a proof that polynomial weights are…
Special functions have been used widely in many problems of applied sciences. However, there are considerable numbers of problems in which exact solutions could not be achieved because of undefined sums or integrals involving special…
A ladder algebraic structure for $L^2(\mathbb{R}^+)$ which closes the Lie algebra $h(1)\oplus h(1)$, where $h(1)$ is the Heisenberg-Weyl algebra, is presented in terms of a basis of associated Laguerre polynomials. Using the Schwinger…
The concept of permutograph is introduced and properties of integral functions on permutographs are established. The central result characterizes the class of integral functions that are representable as lattice polynomials. This result is…
The tridiagonal representation approach is an algebraic method for solving second order differential wave equations. Using this approach in the solution of quantum mechanical problems, we encounter two new classes of orthogonal polynomials…
The distribution function for the first eigenvalue spacing in the Laguerre unitary ensemble of finite size may be expressed in terms of a solution of the fifth Painleve transcendent. The generating function of a certain discontinuous linear…
We consider mixed type multiple orthogonal polynomials associated with a system of weight functions consisting of two vectors. One vector is defined in terms of scaled modified Bessel function of the first kind $I_\mu$ and $I_{\mu+1}$, the…