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.

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.

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 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 Properties of Generalized Gegenbauer Matrix Polynomials

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Ghazala Yasmin
Keyword(s):  
Integral Representation ◽  
Recurrence Relations ◽  
Matrix Polynomials ◽  
Hermite Matrix ◽  
Representation Method ◽  
Generating Matrix

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.

scholarly journals On generalized Laguerre matrix polynomials

2018 ◽  
Vol 10 (1) ◽  
pp. 32-45
Author(s):  
Raed S. Batahan ◽  
A. A. Bathanya
Keyword(s):  
Differential Equation ◽  
Spectral Property ◽  
Recurrence Relation ◽  
Matrix Function ◽  
Recurrence Relations ◽  
Explicit Representation ◽  
Integral Expression ◽  
Matrix Polynomials

Abstract The 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.

scholarly journals On Lommel Matrix Polynomials

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2335
Author(s):  
Ayman Shehata
Keyword(s):  
Entire Function ◽  
Recurrence Relations ◽  
Complex Analysis ◽  
Order Type ◽  
Explicit Representation ◽  
Integral Representations ◽  
Matrix Polynomials ◽  
New Class ◽  
Special Cases ◽  
Matrix Recurrence Relations

The main aim of this paper is to introduce a new class of Lommel matrix polynomials with the help of hypergeometric matrix function within complex analysis. We derive several properties such as an entire function, order, type, matrix recurrence relations, differential equation and integral representations for Lommel matrix polynomials and discuss its various special cases. Finally, we establish an entire function, order, type, explicit representation and several properties of modified Lommel matrix polynomials. There are also several unique examples of our comprehensive results constructed.

scholarly journals On 2-Variables Konhauser Matrix Polynomials and Their Fractional Integrals

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 232 ◽  
Author(s):  
Ahmed Bakhet ◽  
Fuli He
Keyword(s):  
Integral Representations ◽  
Fractional Integrals ◽  
Matrix Polynomials ◽  
Generating Matrix ◽  
Finite Sum

In this paper, we first introduce the 2-variables Konhauser matrix polynomials; then, we investigate some properties of these matrix polynomials such as generating matrix relations, integral representations, and finite sum formulae. Finally, we obtain the fractional integrals of the 2-variables Konhauser matrix polynomials.

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 Note on the Hurwitz–Lerch Zeta Function of Two Variables

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1431
Author(s):  
Junesang Choi ◽  
Recep Şahin ◽  
Oğuz Yağcı ◽  
Dojin Kim
Keyword(s):  
Zeta Function ◽  
Generating Functions ◽  
Recurrence Relations ◽  
Zeta Functions ◽  
Integral Representations ◽  
Lerch Zeta Function ◽  
Derivative Formulas ◽  
The One ◽  
Function Of Two Variables

A number of generalized Hurwitz–Lerch zeta functions have been presented and investigated. In this study, by choosing a known extended Hurwitz–Lerch zeta function of two variables, which has been very recently presented, in a systematic way, we propose to establish certain formulas and representations for this extended Hurwitz–Lerch zeta function such as integral representations, generating functions, derivative formulas and recurrence relations. We also point out that the results presented here can be reduced to yield corresponding results for several less generalized Hurwitz–Lerch zeta functions than the extended Hurwitz–Lerch zeta function considered here. For further investigation, among possibly various more generalized Hurwitz–Lerch zeta functions than the one considered here, two more generalized settings are provided.

On the matrix versions of q-zeta function, q-digamma function and q-polygamma function

2019 ◽  
Vol 13 (08) ◽  
pp. 2050142
Author(s):  
Ravi Dwivedi ◽  
Vivek Sahai
Keyword(s):  
Zeta Function ◽  
Matrix Function ◽  
Integral Representations ◽  
Digamma Function ◽  
Polygamma Function ◽  
The Matrix ◽  
Matrix Series ◽  
Zeta Matrix

This paper deals with the [Formula: see text]-analogues of generalized zeta matrix function, digamma matrix function and polygamma matrix function. We also discuss their regions of convergence, integral representations and matrix relations obeyed by them. We also give a few identities involving digamma matrix function and [Formula: see text]-hypergeometric matrix series.

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