Some Properties of Generalized Gegenbauer Matrix Polynomials

Various new generalized forms of the Gegenbauer matrix polynomials are introduced using the integral representation method, which allows us to express them in terms of Hermite matrix polynomials. Certain properties for these new generalized Gegenbauer matrix polynomials such as recurrence relations and expansion in terms of Hermite matrix polynomials are derived. Further, several families of bilinear and bilateral generating matrix relations for these polynomials are established and their applications are presented.

Q-matrix polynomials in several variables

Filomat ◽

10.2298/fil1509059c ◽

2015 ◽

Vol 29 (9) ◽

pp. 2059-2067 ◽

Cited By ~ 1

Author(s):

Bayram Çekim

Keyword(s):

Matrix Functions ◽

Matrix Polynomials ◽

Several Variables ◽

Hermite Matrix ◽

Q Matrix ◽

In the present paper, we define q-matrix polynomials in several variables which reduces Chan-Chyan-Srivastava and Lagrange-Hermite matrix polynomials in [6]. Then several results involving generating matrix functions for these matrix polynomials are derived.

On new extensions of the generalized Hermite matrix polynomials

Acta et Commentationes Universitatis Tartuensis de Mathematica ◽

10.12697/acutm.2018.22.17 ◽

2019 ◽

Vol 22 (2) ◽

pp. 203-222

Author(s):

Ayman Shehata

Keyword(s):

Integral Representations ◽

Matrix Functions ◽

Matrix Polynomials ◽

Summation Formulae ◽

Summation Formulas ◽

Fractional Calculus Operators ◽

Hermite Matrix ◽

Generating Matrix ◽

Matrix Recurrence Relations

Various families of generating matrix functions have been established in diverse ways. The objective of the present paper is to investigate these generalized Hermite matrix polynomials, and derive some important results for them, such as, the generating matrix functions, matrix recurrence relations, an expansion of xnI, finite summation formulas, addition theorems, integral representations, fractional calculus operators, and certain other implicit summation formulae.

Some new results for Jacobi matrix polynomials

Filomat ◽

10.2298/fil1304713c ◽

2013 ◽

Vol 27 (4) ◽

pp. 713-719 ◽

Cited By ~ 2

Author(s):

Bayram Çekim ◽

Abdullah Altin ◽

Rabia Aktaş

Keyword(s):

Matrix Function ◽

Recurrence Relations ◽

Jacobi Matrix ◽

Integral Representations ◽

Matrix Polynomials ◽

The main aim of this paper is to obtain some recurrence relations and generating matrix function for Jacobi matrix polynomials (JMP). Also, various integral representations satisfied by JMP are derived.

Analytical properties of the two-variables Jacobi matrix polynomials with applications

Demonstratio Mathematica ◽

10.1515/dema-2021-0021 ◽

2021 ◽

Vol 54 (1) ◽

pp. 178-188

Author(s):

Mohamed Abdalla ◽

Muajebah Hidan

Keyword(s):

Recurrence Relations ◽

Jacobi Matrix ◽

Matrix Functions ◽

Type Formula ◽

Matrix Polynomials ◽

Analytical Properties ◽

Abstract In the current study, we introduce the two-variable analogue of Jacobi matrix polynomials. Some properties of these polynomials such as generating matrix functions, a Rodrigue-type formula and recurrence relations are also derived. Furthermore, some relationships and applications are reported.

Two Variables Shivley’s Matrix Polynomials

Symmetry ◽

10.3390/sym11020151 ◽

2019 ◽

Vol 11 (2) ◽

pp. 151 ◽

Cited By ~ 4

Author(s):

Fuli He ◽

Ahmed Bakhet ◽

M. Hidan ◽

M. Abdalla

Keyword(s):

Recurrence Relations ◽

Summation Formula ◽

Matrix Functions ◽

Matrix Polynomials ◽

Special Cases ◽

Generating Matrix ◽

Matrix Recurrence Relations

The principal object of this paper is to introduce two variable Shivley’s matrix polynomials and derive their special properties. Generating matrix functions, matrix recurrence relations, summation formula and operational representations for these polynomials are deduced. Finally, Some special cases and consequences of our main results are also considered.

On Hermite-Hermite matrix polynomials

Mathematica Bohemica ◽

10.21136/mb.2008.140630 ◽

2008 ◽

Vol 133 (4) ◽

pp. 421-434 ◽

Cited By ~ 6

Author(s):

M. S. Metwally ◽

M. T. Mohamed ◽

A. Shehata

Keyword(s):

Matrix Polynomials ◽

Hermite Matrix

Integral Representation Method

Theory of Random Determinants ◽

10.1007/978-94-009-1858-0_8 ◽

1990 ◽

pp. 218-254

Author(s):

V. L. Girko

Keyword(s):

Integral Representation ◽

Representation Method

General Linear Recurrence Sequences and Their Convolution Formulas

Axioms ◽

10.3390/axioms8040132 ◽

2019 ◽

Vol 8 (4) ◽

pp. 132 ◽

Cited By ~ 2

Author(s):

Paolo Emilio Ricci ◽

Pierpaolo Natalini

Keyword(s):

Generating Functions ◽

Recurrence Relations ◽

Second Order ◽

General Linear ◽

Linear Recurrence ◽

Order Linear ◽

Matrix Polynomials ◽

Recurrence Sequences ◽

Straightforward Extension

We extend a technique recently introduced by Chen Zhuoyu and Qi Lan in order to find convolution formulas for second order linear recurrence polynomials generated by 1 1 + a t + b t 2 x . The case of generating functions containing parameters, even in the numerator is considered. Convolution formulas and general recurrence relations are derived. Many illustrative examples and a straightforward extension to the case of matrix polynomials are shown.