Certain Properties of Generalized Hermite-Type Matrix Polynomials Using Weisner’s Group Theoretic Techniques

Shehata, Ayman

doi:10.1007/s00574-018-0108-6

Cited by 4 publications

(3 citation statements)

References 16 publications

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“…Focusing on practical applications, one realizes that the use of new classes of special matrix functions in certain physical problems has led to solutions that are difficult to obtain using traditional analytical and numerical methods. In this context, Hermite, Chebyshev, Jacobi, Laguerre, and Gegenbauer matrix polynomials have been introduced and studied (see, e.g., [13][14][15][16][17]).…”

Section: Introductionmentioning

confidence: 99%

On the Two-Variable Analogue Matrix of Bessel Polynomials and Their Properties

Bakhet,

Hussain,

Niyaz

et al. 2024

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In this paper, we explore a study focused on a two-variable extension of matrix Bessel polynomials. We initiate the discussion by introducing the matrix Bessel polynomials involving two variables and derive specific differential formulas and recurrence relations associated with them. Additionally, we present a segment detailing integral formulas for the extended matrix Bessel polynomials. Lastly, we introduce the Laplace–Carson transform for the two-variable matrix Bessel polynomial analogue.

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Section: Introductionmentioning

confidence: 99%

On the Two-Variable Analogue Matrix of Bessel Polynomials and Their Properties

Bakhet,

Hussain,

Niyaz

et al. 2024

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“…One of these special equations is the Hermite equations. Hermite equations have many real world practical applications [27]- [33]. We will only focus on the methods of solution and use in a mathematical sense.…”

Section: Introductionmentioning

confidence: 99%

Some Spectral Properties of Multiplicative Hermite Equation

Goktas

Yılmaz

YAR

2022

Fundamental Journal of Mathematics and Applications

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We reconstruct the Multiplicative Hermite Equation from multiplicative Sturm-Liouville equation. A new representation of eigenfunctions for the constructed problem are obtained by the power series solution technique. While making these solutions, multiplicative Hermite polynomials were used strongly. We get a generator for multiplicative Hermite polynomials and construct integration representations for these polynomials. Finally, some spectral properties of the multiplicative Hermite problem are examined in detail.

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“…Miller also extends Weisner's theory by relating it to what? Recently the matrix analogues of Laguerre and modified Laguerre matrix polynomials have been considered in [5,6,7,16,17] for matrices in C N ×N in a number of previous papers, see for example [1,14,15] and his work references therein [18,19,20].…”

Section: Introductionmentioning

confidence: 99%

Certain Generating Matrix Functions of Charlier Matrix Polynomials Using Weisner's Group Theoretic Method

Shehata¹

2019

Preprint

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The present paper discusses a study of a class of Charlier matrix polynomials and its generalized analogue. Certain generating matrix functions, recurrence matrix relations, matrix differential equation, summation formulas and many new results have been discussed for these matrix polynomials. Weisner's group theoretic method is used to obtain matrix generating relations for Charlier matrix polynomials and the details of this method were given in this paper. Finally, we will discuss only briefly the procedure followed.

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Certain Properties of Generalized Hermite-Type Matrix Polynomials Using Weisner’s Group Theoretic Techniques

Cited by 4 publications

References 16 publications

On the Two-Variable Analogue Matrix of Bessel Polynomials and Their Properties

On the Two-Variable Analogue Matrix of Bessel Polynomials and Their Properties

Some Spectral Properties of Multiplicative Hermite Equation

Certain Generating Matrix Functions of Charlier Matrix Polynomials Using Weisner's Group Theoretic Method

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