Related papers: Integrals Involving Associated Laguerre Polynomial…
New expressions for Laguerre and Hermite polynomials are shown. They are based on operator algebras commonly used in quantum mechanics.
Laguerre and Laguerre-type polynomials are orthogonal polynomials on the interval $[0,\infty)$ with respect to a weight function of the form $w(x) = x^{\alpha} e^{-Q(x)}, Q(x) = \sum_{k=0}^m q_k x^k, \alpha > -1, q_m > 0$. The classical…
We give presentation of composition inverse of formal power serie in a logarithmic form.
Using a new result on the integral involving the product of Bessel functions and associated Laguerre polynomials, published in the mathematical literature some time ago, we present an alternative method for calculating discrete-discrete…
In this paper, we study the boundedness of a class of fractional integrals and derivatives associated with Laguerre polynomial expansions on Laguerre Lipschitz spaces. The consideration of such operators is motivated by the study of…
From an identity connecting a combinatorial sum and Legendre polynomials, we derive closed forms for a number of combinatorial sums. Some of them are obtained via results about the integrals of functions associated with Legendre…
In this paper we introduce a version of irreducible Laguerre polynomials in two variables and prove for it a congruence property, which is similar to the one obtained by Carlitz for the classical Laguerre polynomials in one variable.
A simple procedure to obtain complete, closed expressions for Lie algebra invariants is presented. The invariants are ultimately polynomials in the group parameters. The construction of finite group elements require the use of projectors,…
In this paper we consider sequences of polynomials orthogonal with respect to certain discrete Laguerre-Sobolev inner product, with two perturbations (involving derivatives) located inside the oscillatory region for the classical Laguerre…
Explicit forms are given of matrix elements of generalized coherent operators based on Lie algebras su(1,1) and su(2). We also give a kind of factorization formula of the associated Laguerre polynomials.
Matrix valued Laguerre polynomials are introduced via a matrix weight function involving several degrees of freedom using the matrix nature. Under suitable conditions on the parameters the matrix weight function satisfies matrix Pearson…
The aim of this paper is to introduce the degenerate generalized Laguerre polynomials as the degenerate version of the generalized Laguerre polynomials and to derive some properties related to those polynomials and Lah numbers, including an…
A semi-discrete Lax pair formed from the differential system and recurrence relation for semi-classical orthogonal polynomials, leads to a discrete integrable equation for a specific semi-classical orthogonal polynomial weight. The main…
We establish closed-form expansions for the universal edge elimination polynomial of paths and cycles and their generating functions. This includes closed-form expansions for the bivariate matching polynomial, the bivariate chromatic…
We give a closed formula of the Littlewood-Richardson coefficients.
We give evaluations in closed form of certain Lehmer-binomial series
The integral representation of the Hadamard product of two functions is used to prove several Euler-type series transformation formulas. As applications we obtain three binomial identities involving harmonic numbers and an identity for the…
We give new explicit representations as well as new generating functions for the associated Meixner, Charlier, Laguerre, and Krawtchouk polynomials. The obtained results are then used to derive new generating functions and convolution-type…
In this paper, we investigate some identities of Laguerre polynomials involving Bernoulli and Euler polynomials which are derived from umbral calculus.
The pure time delay operator is considered in continuous and discrete time under the assumption of the input signal being integrable (summable) with square. By making use of a discrete convolution operator with polynomial Markov parameters,…