Chebyshev-type Matrix Polynomials and Integral Transforms

Kargın, Levent; Kurt, Veli

doi:10.15672/hjms.2015449102

Cited by 10 publications

(7 citation statements)

References 13 publications

(9 reference statements)

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“…We note that taking A D OE1 1 1 , m D 2 and replacing xI by x q A 2 ; the expressions (3.8) and (3.9) coincide with the formulas which was given in [24] for the second kind Chebyshev matrix polynomials.…”

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confidence: 60%

On generalized Humbert matrix polynomials

Kargın¹,

Kurt²

2014

MMN

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Aktaş et. al. in [3] introduced the generalized Humbert matrix polynomials (G-HMP) P A n .m; x; y; c/. In this paper we focus on some properties of these matrix polynomials such as matrix recurrence relations, matrix differential equation and an integral representation. We introduce generalized forms of operational rules associated with operators corresponding to a G-HMP expansions. Moreover, we obtain a series transformation formula involving Gegenbauer matrix polynomials. Then we provide a number of applications.

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confidence: 60%

On generalized Humbert matrix polynomials

Kargın¹,

Kurt²

2014

MMN

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“…Recently, considerable attention has been paid to fractional integrals associated with special matrix functions and orthogonal matrix polynomials, due mainly to their usefulness and applications in various research subjects (see, e.g., [8,14,18,19,[36][37][38][39][40][41][42][43][44][45] and the references cited therein). [46] investigated the revival of the Bessel polynomials and the generalized Bessel polynomials (GBPs) whose explicit forms are given, respectively, by…”

Section: Introductionmentioning

confidence: 99%

Certain Matrix Riemann–Liouville Fractional Integrals Associated with Functions Involving Generalized Bessel Matrix Polynomials

2021

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The fractional integrals involving a number of special functions and polynomials have significant importance and applications in diverse areas of science; for example, statistics, applied mathematics, physics, and engineering. In this paper, we aim to introduce a slightly modified matrix of Riemann–Liouville fractional integrals and investigate this matrix of Riemann–Liouville fractional integrals associated with products of certain elementary functions and generalized Bessel matrix polynomials. We also consider this matrix of Riemann–Liouville fractional integrals with a matrix version of the Jacobi polynomials. Furthermore, we point out that a number of Riemann–Liouville fractional integrals associated with a variety of functions and polynomials can be presented, which are presented as problems for further investigations.

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“…The study of special matrix polynomials and orthogonal matrix polynomials is important due to their applications in certain areas of statistics, physics, engineering, Lie groups theory, group representation theory and differential equations. Recently, Significant results emerged in the classical theory of orthogonal polynomials and special functions have been expanded to include many orthogonal matrix limits and special matrix functions and applications that have continued to appear in the literature until now (see for example [1,4,5,6,7,11,13,14,15,16,17,18,19,20,27,30,31,32,33,34,36]).…”

Section: Introductionmentioning

confidence: 99%

An extension of basic Humbert hypergeometric functions

Shehata¹

2021

Preprint

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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.

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Chebyshev-type Matrix Polynomials and Integral Transforms

Cited by 10 publications

References 13 publications

On generalized Humbert matrix polynomials

On generalized Humbert matrix polynomials

Certain Matrix Riemann–Liouville Fractional Integrals Associated with Functions Involving Generalized Bessel Matrix Polynomials

An extension of basic Humbert hypergeometric functions

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