scholarly journals On the Extended Hypergeometric Matrix Functions and Their Applications for the Derivatives of the Extended Jacobi Matrix Polynomial

2020 ◽  
Vol 2020 ◽  
pp. 1-8 ◽  
Author(s):  
Fuli He ◽  
Ahmed Bakhet ◽  
M. Abdalla ◽  
M. Hidan
Keyword(s):  
Matrix Function ◽  
Matrix Polynomial ◽  
Jacobi Matrix ◽  
Integral Representations ◽  
Matrix Functions ◽  
Matrix Polynomials ◽  
Special Cases ◽  
Generating Matrix Functions ◽  
Generating Matrix ◽  
Derivatives Of

In this paper, we obtain some generating matrix functions and integral representations for the extended Gauss hypergeometric matrix function EGHMF and their special cases are also given. Furthermore, a specific application for the extended Gauss hypergeometric matrix function which includes Jacobi matrix polynomials is constructed.

scholarly journals On new extensions of the generalized Hermite matrix polynomials

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 ◽  
Generating Matrix Functions ◽  
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.

scholarly journals Some new results for Jacobi matrix polynomials

Filomat ◽  
2013 ◽  
Vol 27 (4) ◽  
pp. 713-719 ◽  
Author(s):  
Bayram Çekim ◽  
Abdullah Altin ◽  
Rabia Aktaş
Keyword(s):  
Matrix Function ◽  
Recurrence Relations ◽  
Jacobi Matrix ◽  
Integral Representations ◽  
Matrix Polynomials ◽  
Generating Matrix

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

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 ◽  
Generating Matrix Functions ◽  
Generating Matrix

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.

scholarly journals Two Variables Shivley’s Matrix Polynomials

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 151 ◽  
Author(s):  
Fuli He ◽  
Ahmed Bakhet ◽  
M. Hidan ◽  
M. Abdalla
Keyword(s):  
Recurrence Relations ◽  
Summation Formula ◽  
Matrix Functions ◽  
Matrix Polynomials ◽  
Special Cases ◽  
Generating Matrix Functions ◽  
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.

scholarly journals Q-matrix polynomials in several variables

Filomat ◽  
2015 ◽  
Vol 29 (9) ◽  
pp. 2059-2067 ◽  
Author(s):  
Bayram Çekim
Keyword(s):  
Matrix Functions ◽  
Matrix Polynomials ◽  
Several Variables ◽  
Generating Matrix Functions ◽  
Hermite Matrix ◽  
Q Matrix ◽  
Generating 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.

scholarly journals Analytical Properties of the Generalized Heat Matrix Polynomials Associated with Fractional Calculus

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Mohamed Abdalla ◽  
Salah Mahmoud Boulaaras
Keyword(s):  
Fractional Calculus ◽  
Integral Transforms ◽  
Matrix Functions ◽  
Matrix Polynomials ◽  
Matrix Version ◽  
Analytical Properties ◽  
Fractional Calculus Operators ◽  
Finite Sums ◽  
Generating Matrix Functions ◽  
Generating Matrix

In this paper, we introduce a matrix version of the generalized heat polynomials. Some analytic properties of the generalized heat matrix polynomials are obtained including generating matrix functions, finite sums, and Laplace integral transforms. In addition, further properties are investigated using fractional calculus operators.

scholarly journals Modified Laguerre matrix polynomials

Filomat ◽  
2014 ◽  
Vol 28 (10) ◽  
pp. 2069-2076 ◽  
Author(s):  
Levent Kargin ◽  
Veli Kurt
Keyword(s):  
Differential Equation ◽  
Explicit Expression ◽  
Matrix Functions ◽  
Series Solutions ◽  
Matrix Differential Equation ◽  
Rodrigues Formula ◽  
Matrix Polynomials ◽  
Generating Matrix Functions ◽  
Generating Matrix ◽  
Matrix Differential

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.

scholarly journals Certain Generating Matrix Functions of Charlier Matrix Polynomials Using Weisner's Group Theoretic Method

2019 ◽  
Author(s):  
Ayman Shehata
Keyword(s):  
Matrix Functions ◽  
Matrix Differential Equation ◽  
Theoretic Method ◽  
Matrix Polynomials ◽  
Summation Formulas ◽  
Group Theoretic Method ◽  
Generating Relations ◽  
Generating Matrix Functions ◽  
Generating Matrix ◽  
Matrix Differential

The present paper discusses a study of a class of Charlier matrix polynomials and its generalized analogue. Certain generating matrix functions, recurrence matrix relations, matrix differential equation, summation formulas and many new results have been discussed for these matrix polynomials. Weisner's group theoretic method is used to obtain matrix generating relations for Charlier matrix polynomials and the details of this method were given in this paper. Finally, we will discuss only briefly the procedure followed.

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