in this paper, we give some determinantal and permanental representations of generalized lucas polynomials, which are a general form of generalized bivariate lucas p-polynomials, ordinary lucas and perrin sequences etc., by using various hessenberg matrices. in addition, we show that determinant and permanent of these hessenberg matrices can be obtained by using combinations. then we show, the ...

A calculation of the linearization coefficients of the (generalized) Laguerre polynomials L")(x) is proposed by means of analytic and combinatorial methods. This paper extends to the case of an arbitrary a a combinatoric and analytic result due to Askey, Ismail, and Koornwinder and Even and Gillis. Theorem (/-extension) AMS(MOS) subject classifications. 33A65, 05A 15 1. Introduction. Let (p,,(x...

Based on the generalized extended beta function, we shall introduce and study a new hypergeometric-type zeta function together with related integral representations, differential relations, finite sums, series expansions. Also, present relationship between Laguerre polynomials. Our hypergeometric type involves several known functions including Riemann, Hurwitz, Hurwitz-Lerch, Barnes as particul...

The object of this paper is to prove combinatorially several (13 of them) limit formulas relating different families of hypergeometric orthogonal polynomials in Askey’s chart classifying them. We first find a combinatorial model for Hahn polynomials which, as pointed out by Foata at the ICM (1983), “contains” models for Jacobi, Meixner, Krawtchouk, Laguerre and Charlier polynomials. Seven limit...

In this paper, a numerical method, which is called the Laguerre collocation method, for the approximate solution of Lane–Emden type functional differential equations in terms of Laguerre polynomials are derived. The method is based on the matrix relations of Laguerre polynomials and their derivatives, and reduces the solution of the Lane–Emden type functional differential equation to the soluti...

We investigate some properties of non-symmetric Jack, Hermite and Laguerre polynomials which occur as the polynomial part of the eigenfunctions for certain Calogero-Sutherland models with exchange terms. For the non-symmetric Jack polynomials, the constant term normalization N is evaluated using recurrence relations, and N is related to the norm for the non-symmetric analogue of the power-sum i...

We investigate some properties of non-symmetric Jack, Hermite and Laguerre polynomials which occur as the polynomial part of the eigenfunctions for certain Calogero-Sutherland models with exchange terms. For the non-symmetric Jack polynomials, the constant term normalization N η is evaluated using recurrence relations, and N η is related to the norm for the non-symmetric analogue of the power-s...

Many limits are known for hypergeometric orthogonal polynomials that occur in the Askey scheme. We show how asymptotic representations can be derived by using the generating functions of the polynomials. For example, we discuss the asymptotic representation of the Meixner-Pollaczek, Jacobi, Meixner, and Krawtchouk polynomials in terms of Laguerre polynomials.

The monomiality principle was introduced (see e.g. [1] and the references therein) in order to derive properties of special polynomials from the corresponding ones holding for monomials. A set of paramount importance in this framework is given by the Hermite-Kampé de Fériet (shortly H-KdF) or Gould-Hopper polynomials [2], [3], [4]. As it is well known, the Hermite-Kampé de Fériet polynomials H ...

has been prepared by th e National Bureau of Standards [1]; 1 th e introduction to the table gives a precise definition of this function. This table covers the range Ixl ~ 20, Iyl ~ 20, with argumcnts variously spaced. In order to compute E1( z) olltsid e this range, (or within this range, a t points where interpolation is awkward, which are those with comparatively large argument), several met...