Nonnegative linearization coefficients of the generalized Bessel polynomials

Tcheutia, Daniel Duviol

doi:10.1007/s11139-018-0006-y

Cited by 5 publications

(7 citation statements)

References 22 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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“…Remark 2.2. If the matrix F, L ∈ C 1×1 = C, then the generalized Bessel matrix polynomial in (2.15) reduces to generalized Bessel polynomial in [10][11][12].…”

Section: Auxiliary Toolboxmentioning

confidence: 99%

“…In [4], extension to the matrix framework of the classical families of Legendre, Laguerre, Jacobi, Chebyshev, Gegenbaner and Hermite polynomials have been introduced. 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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“…Recently, these polynomials have been investigated in diverse ways and turned out to be applicable in a number of research fields (see, to exemplify, [22][23][24][25]).…”

Section: Introductionmentioning

confidence: 99%

On Behavior Laplace Integral Operators with Generalized Bessel Matrix Polynomials and Related Functions

Hidan

Akel

Boulaaras

et al. 2021

Journal of Function Spaces

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Recently, the applications and importance of integral transforms (or operators) with special functions and polynomials have received more attention in various fields like fractional analysis, survival analysis, physics, statistics, and engendering. In this article, we aim to introduce a number of Laplace and inverse Laplace integral transforms of functions involving the generalized and reverse generalized Bessel matrix polynomials. In addition, the current outcomes are yielded to more outcomes in the modern theory of integral transforms.

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Nonnegative linearization coefficients of the generalized Bessel polynomials

Cited by 5 publications

References 22 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

On Behavior Laplace Integral Operators with Generalized Bessel Matrix Polynomials and Related Functions

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