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 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 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.

scholarly journals Generalization of Konhauser Polynomials

2020 ◽  
Vol 2 (11) ◽  
pp. 8-14
Keyword(s):  
Generating Functions ◽  
Recurrence Relations ◽  
Biorthogonal System ◽  
Integral Representations ◽  
New Class ◽  
Generating Relations ◽  
Biorthogonal Polynomials

In this paper, we are showing study of biorthogonal polynomials associated with generalization of Laguere polynomials of Srivastava and Singhal [14]. It happens to generalized Konhauser. here we are trying to obtain the generating functions, recurrence relations, biorthogonality relations, integral representations and also bilinear and bilateral generating relations for the new class of biorthogonal system.

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 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 Some Characterizations of the Extended Beta and Gamma Functions: Properties and Applications

2021 ◽  
pp. 101-112
Keyword(s):  
Recurrence Relations ◽  
Integral Representations ◽  
General Introduction ◽  
Differentiation Formula ◽  
Gamma Functions ◽  
Definite Integrals ◽  
Special Cases ◽  
Form Representation ◽  
Basic Functions ◽  
Extended Function

The article represents the elementary and general introduction of some characterizations of the extended gamma and beta Functions and their important properties with various representations. This paper provides reviews of some of the new proposals to extend the form of basic functions and some closed-form representation of more integral functions is described. Some of the relative behaviors of the extended function, the special cases resulting from them when fixing the parameters, the decomposition equation, the integrative representation of the proposed general formula, the correlations related to the proposed formula, the frequency relationships, and the differentiation equation for these basic functions were investigated. We also investigated the asymptotic behavior of some special cases, known formulas, the basic decomposition equation, integral representations, convolutions, recurrence relations, and differentiation formula for these target functions by studying. Applications of these functions have been presented in the evaluation of some reversible Laplace transforms to the complex of definite integrals and the infinite series of related basic functions.

scholarly journals A new extension of Srivastava’s triple hypergeometric functions and their associated properties

Analysis ◽  
2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Abdus Saboor ◽  
Gauhar Rahman ◽  
Zunaira Anjum ◽  
Kottakkaran Sooppy Nisar ◽  
Serkan Araci
Keyword(s):  
Hypergeometric Functions ◽  
Recurrence Relations ◽  
Integral Representations ◽  
Pochhammer Symbol ◽  
Basic Properties ◽  
Special Cases ◽  
Derivative Formulas

AbstractIn this paper, we define a new extension of Srivastava’s triple hypergeometric functions by using a new extension of Pochhammer’s symbol that was recently proposed by Srivastava, Rahman and Nisar [H. M. Srivastava, G. Rahman and K. S. Nisar, Some extensions of the Pochhammer symbol and the associated hypergeometric functions, Iran. J. Sci. Technol. Trans. A Sci. 43 2019, 5, 2601–2606]. We present their certain basic properties such as integral representations, derivative formulas, and recurrence relations. Also, certain new special cases have been identified and some known results are recovered from main results.

New family of Whitney numbers

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 309-320 ◽  
Author(s):  
B.S. El-Desouky ◽  
Nenad Cakic ◽  
F.A. Shiha
Keyword(s):  
Generating Functions ◽  
Recurrence Relations ◽  
Stirling Numbers ◽  
Explicit Formulas ◽  
Basic Properties ◽  
New Family ◽  
Whitney Numbers ◽  
Special Cases

In this paper we give a new family of numbers, called ??-Whitney numbers, which gives generalization of many types of Whitney numbers and Stirling numbers. Some basic properties of these numbers such as recurrence relations, explicit formulas and generating functions are given. Finally many interesting special cases are derived.

scholarly journals Survival and Reliability Analysis with an Epsilon-Positive Family of Distributions with Applications

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 908
Author(s):  
Perla Celis ◽  
Rolando de la Cruz ◽  
Claudio Fuentes ◽  
Héctor W. Gómez
Keyword(s):  
Survival Data ◽  
Maximum Likelihood Estimates ◽  
New Class ◽  
New Family ◽  
Gamma Distributions ◽  
Special Cases ◽  
Log Normal ◽  
Positive Support ◽  
Positive Distributions ◽  
Family Of Distributions

We introduce a new class of distributions called the epsilon–positive family, which can be viewed as generalization of the distributions with positive support. The construction of the epsilon–positive family is motivated by the ideas behind the generation of skew distributions using symmetric kernels. This new class of distributions has as special cases the exponential, Weibull, log–normal, log–logistic and gamma distributions, and it provides an alternative for analyzing reliability and survival data. An interesting feature of the epsilon–positive family is that it can viewed as a finite scale mixture of positive distributions, facilitating the derivation and implementation of EM–type algorithms to obtain maximum likelihood estimates (MLE) with (un)censored data. We illustrate the flexibility of this family to analyze censored and uncensored data using two real examples. One of them was previously discussed in the literature; the second one consists of a new application to model recidivism data of a group of inmates released from the Chilean prisons during 2007. The results show that this new family of distributions has a better performance fitting the data than some common alternatives such as the exponential distribution.

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