Operational formula for the generalized Bessel matrix polynomials

Abdalla, Mohamed

doi:10.20454/jmmnm.2017.1316

Cited by 5 publications

(10 citation statements)

References 10 publications

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“…Very recently, these polynomials have been studied in diverse ways and have turned out to be applicable in a number of research fields (see, e.g., [8,[47][48][49]). Among various extensions of the classical orthogonal polynomials to the matrix setting, the generalized and reverse-generalized Bessel matrix polynomials have been presented and studied in diverse ways (see, e.g., [37]; see also [50][51][52]).…”

Section: Krall and Frinkmentioning

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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Section: Krall and Frinkmentioning

confidence: 99%

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

2021

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“…Definition 2.6. [4,13,16] Let F and L be commuting matrices in C n×n such that L is an invertible matrix. For any natural number n ∈ N 0 , the n-th generalized Bessel matrix polynomial Y n (ξ; F, L) is defined as…”

Section: Auxiliary Toolboxmentioning

confidence: 99%

“…Meanwhile, one particular orthogonal polynomials which frequently appears in the recent studies and applications [10][11][12], is the generalized Bessel polynomials, which in its matrix form is also defined in [4,13]. Later on, distinct works of the generalized Bessel matrix polynomials have been discussed (see [14][15][16][17]).…”

Section: Introductionmentioning

confidence: 99%

Computation of Fourier transform representations involving the generalized Bessel matrix polynomials

Abdalla

2021

Preprint

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Motivated by the recent studies and developments of the integral transforms with various special matrix functions, including the matrix orthogonal polynomials as kernels. In this article, we derive the formulas for Fourier cosine transforms and Fourier sine transforms of matrix functions involving generalized Bessel matrix polynomials. With the help of these transforms a number of results are considered which are extensions of the corresponding results in the standard cases. The results given here are of general character and can yield a number of (known and new) results in modern integral transforms.

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“…Meanwhile, one particular orthogonal polynomial family which frequently appears in the recent studies and applications [10][11][12] is that of generalized Bessel polynomials, which in its matrix form is also defined in [4,13]. Later on, distinct works on the generalized Bessel matrix polynomials have been discussed (see [14][15][16][17]).…”

Section: Introductionmentioning

confidence: 99%

Computation of Fourier transform representations involving the generalized Bessel matrix polynomials

Abdalla

Akel

2021

Adv Differ Equ

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Motivated by the recent studies and developments of the integral transforms with various special matrix functions, including the matrix orthogonal polynomials as kernels, in this article we derive the formulas for Fourier cosine and sine transforms of matrix functions involving generalized Bessel matrix polynomials. With the help of these transforms several results are obtained, which are extensions of the corresponding results in the standard cases. The results given here are of general character and can yield a number of (known and new) results in modern integral transforms.

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Operational formula for the generalized Bessel matrix polynomials

Abstract: In this paper, we propose to give some operational formula of the generalized Bessel matrix polynomials (GBMPs) using the difference operators. Some expansions of the results are also established.

Cited by 5 publications

References 10 publications

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

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

Computation of Fourier transform representations involving the generalized Bessel matrix polynomials

Computation of Fourier transform representations involving the generalized Bessel matrix polynomials

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