Laguerre Matrix Polynomials Research Articles

Some Relations on the rRs(P,Q,z) Matrix Function

In this paper, we derive some classical and fractional properties of the rRs matrix function by using the Hilfer fractional operator. The theory of special matrix functions is the theory of those matrices that correspond to special matrix functions such as the gamma, beta, and Gauss hypergeometric matrix functions. We will also show the relationship with other generalized special matrix functions in the context of the Konhauser and Laguerre matrix polynomials.

Q-Analogue Modified Laguerre Matrix Polynomials of Three Variables

In this paper, the q-analogue modified Laguerre matrix polynomials of three variables are introduced as finite series and Some properties of these matrix polynomials are obtained.

On certain Konhauser and Laguerre matrix polynomials

In this paper, we generalize the well-known Laguerre and Konhauser matrix polynomials, given by Shehata (12), varma and Tas (14), respectively, and we also introduced a set of new Laguerre matrix polynomials \(L_n^{(B,C)} (α,x)\), we also obtained some generating relations and integral representations for these sets of polynomials.

On generalized Laguerre matrix polynomials

AbstractThe main object of the present paper is to introduce and study the generalized Laguerre matrix polynomials for a matrix that satisfies an appropriate spectral property. We prove that these matrix polynomials are characterized by the generalized hypergeometric matrix function. An explicit representation, integral expression and some recurrence relations in particular the three terms recurrence relation are obtained here. Moreover, these matrix polynomials appear as solution of a differential equation.

Lie algebra and Laguerre Matrix Polynomials of One Variable

Lie algebra and Laguerre Matrix Polynomials of One Variable

Pseudo Laguerre Matrix Polynomials, Operational Identities and Quasi-Monomiality

The main purpose of this paper is to introduce the matrix extension of the pseudo Laguerre matrix polynomials and to explore the formal properties of the operational rules and the principle of quasi-monomiality to derive a number of properties for pseudo Laguerre matrix polynomials.

Lie algebra and Laguerre Matrix Polynomials of One Variable

Lie algebra and Laguerre Matrix Polynomials of One Variable

A note on two variable Laguerre matrix polynomials

The principal object of this paper is to present a natural further step toward the mathematical properties and presentations concerning the two variable Laguerre matrix polynomials defined in (Bin-Saad, Maged G., Antar, A. Al-Sayaad, 2015. Study of two variable Laguerre polynomials via symbolic operational images. Asian J. of math. and comput. research, 2(1), 42–50). Series expansions, integral transforms and bilinear and bilateral generating matrix functions for these polynomials are established. Some particular cases and consequences of our main results are also considered.

The q-Laguerre matrix polynomials.

The Laguerre polynomials have been extended to Laguerre matrix polynomials by means of studying certain second-order matrix differential equation. In this paper, certain second-order matrix q-difference equation is investigated and solved. Its solution gives a generalized of the q-Laguerre polynomials in matrix variable. Four generating functions of this matrix polynomials are investigated. Two slightly different explicit forms are introduced. Three-term recurrence relation, Rodrigues-type formula and the q-orthogonality property are given.

A new relation including2F2 between Laguerre and Hermite matrix polynomials

Abstract In the present paper, a new relation including hypergeometric matrix function between Laguerre and Hermite matrix polynomials presented in [2,3] is derived.

Hermite–Laguerre Matrix Polynomials and Generating Relations

The Hermite–Laguerre matrix polynomials and the Hermite-modified Laguerre matrix polynomials are introduced. Certain generating relations for the Hermite–Laguerre matrix polynomials are derived by using operational methods. Some results for the matrix and scalar special polynomials related to these new special matrix polynomials are also obtained as applications.

Modified Laguerre matrix polynomials

In this paper, modified Laguerre matrix polynomials which appear as finite series solutions of second-order matrix differential equation are introduced. Some formulas related to an explicit expression, a three-term matrix recurrence relation and a Rodrigues formula are obtained. Several families of bilinear and bilateral generating matrix functions for modified Laguerre matrix polynomials are derived. Finally a new generalization of the Laguerre-type matrix polynomials is introduced.

Application of Laguerre matrix polynomials to the numerical inversion of Laplace transforms of matrix functions

This paper presents an application of Laguerre matrix polynomial series to the numerical inversion of Laplace transforms of matrix functions.

2-variable Laguerre matrix polynomials and Lie-algebraic techniques**This work has been done under a Major Research Project no F.33-110/2007 (SR) sanctioned to the first author by the University Grants Commission, Government of India, New Delhi.

The authors introduce 2-variable forms of Laguerre and modified Laguerre matrix polynomials and derive their special properties. Further, the representations of the special linear Lie algebra sl(2) and the harmonic oscillator Lie algebra are used to derive certain results involving these polynomials. Furthermore, the generating relations for the ordinary as well as matrix polynomials related to these matrix polynomials are derived as applications.

A note on Sobolev orthogonality for Laguerre matrix polynomials

Let {L (A,λ) n (x)} n⩾0 be the sequence of monic Laguerre matrix polynomials defined on [0, ∞) by $$L_n ^{(A,\lambda )} (x) = \frac{{n!}}{{( - \lambda )^n }}\sum\limits_{k = 0}^n {\frac{{( - \lambda )^k }}{{k!(n - k)!}}(A + I)_n [(A + I)_k ]^{ - 1} x^k } ,$$ where A ∈ Cr×r. It is known that {L (A,λ) n (x)} n⩾0 is orthogonal with respect to a matrix moment functional when A satisfies the spectral condition that Re(z) > −1 for every z ∈ σ(A).In this note we show that for A such that σ(A) does not contain negative integers, the Laguerre matrix polynomials L (A,λ) n (x) are orthogonal with respect to a non-diagonal Sobolev-Laguerre matrix moment functional, which extends two cases: the above matrix case and the known scalar case.

Laguerre matrix polynomial series expansion: Theory and computer applications

This paper deals with the expansion of matrix functions in series of Laguerre matrix polynomials of a complex matrix parameter. A new asymptotic expression for positive and large x and n is obtained for this family of matrix polynomials that improves previous existing expressions. This expression is applied to improving the conditions imposed on the matrix function that are to be expanded in a series of non-hermitian Laguerre matrix polynomials, providing a new series expansion theorem that is more general than previous works. An application to solving linear differential systems without matrix exponentials is included.

On the asymptotics of Laguerre matrix polynomials for large [formula omitted] and [formula omitted

This work deals with the asymptotics of normalized Laguerre matrix polynomials of a complex matrix parameter for n / x = o ( 1 ) and x / n = O ( 1 ) as n → ∞ .

Asymptotic expressions of certain type of matrix integrals

This paper deals with the asymptotic expression of parametric matrix integrals related to Laguerre's matrix polynomials using path integration of matrix valued functions.

The growth of laguerre matrix polynomials on bounded intervals

Let A be a matrix in C r×r such that Re(z) > −1 2 for all the eigenvalues of A and let {π n ( A, 1 2 ) (x)} be the normalized sequence of Laguerre matrix polynomials associated with A. In this paper, it is proved that π n (A, 1 2 ) (x) = O(n α(A)/2 ln r−1(n)) and π n+1 (A, 1 2 ) (x) − π n (A, 1 2 ) (x) = O(n (α(A)−1)/2 ln r−1(n)) uniformly on bounded intervals, where α( A) = max{Re( z); z eigenvalue of A}.

Laguerre matrix polynomials and systems of second-order differential equations

In this paper we introduce the class of Laguerre matrix polynomials which appears as finite series solutions of second-order matrix differential equations of the form tX″ +( A + I − λtI) X′ + CX = 0. An explicit expression for the Laguerre matrix polynomials, a three-term matrix recurrence relation, a Rodrigues formula and orthogonality properties are given.