Extended Gauss Hypergeometric Matrix Functions

Abdalla, Mohamed; Bakhet, Ahmed

doi:10.1007/s40995-017-0183-3

Cited by 32 publications

(35 citation statements)

References 9 publications

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“…In the past few years, matrix functions and polynomials defined in terms of power matrix series [18][19][20][21] attracted the attention to new and exciting problems, specifically that involve the generalized hypergeometric matrix functions and future directions. It is worth mentioning the recent work of Shang [22] who uncovered some of the information of topological properties hidden in the smaller eigenvalues of A in matrix functions of the form f (A) = ∑ ∞ k=0 c k A k .…”

Section: Introductionmentioning

confidence: 99%

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On the Fractional Order Rodrigues Formula for the Shifted Legendre-Type Matrix Polynomials

et al. 2020

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The generalization of Rodrigues’ formula for orthogonal matrix polynomials has attracted the attention of many researchers. This generalization provides new integral and differential representations in addition to new mathematical results that are useful in theoretical and numerical computations. Using a recently studied operational matrix for shifted Legendre polynomials with the variable coefficients fractional differential equations, the present work introduces the shifted Legendre-type matrix polynomials of arbitrary (fractional) orders utilizing some Rodrigues matrix formulas. Many interesting mathematical properties of these matrix polynomials are investigated and reported in this paper, including recurrence relations, differential properties, hypergeometric function representation, and integral representation. Furthermore, the orthogonality property of these polynomials is examined in some particular cases. The developed results provide a matrix framework that generalizes and enhances the corresponding scalar version and introduces some new properties with proposed applications. Some of these applications are explored in the present work.

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Section: Introductionmentioning

confidence: 99%

“…Recently, many authors (see, e.g., [18][19][20][21]) proposed the extension of the classical polynomials to the matrix framework. The operational matrix of fractional derivatives has been studied for various types of orthogonal polynomials, including Chebyshev polynomials [27].…”

Section: Introductionmentioning

confidence: 99%

On the Fractional Order Rodrigues Formula for the Shifted Legendre-Type Matrix Polynomials

et al. 2020

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“…The generalization of special functions to matrix valued functions is a growing subject and the first Kummer function has been studied widely (see [4][5][6][7]). However, the second Kummer function has not yet been examined.…”

Section: Introductionmentioning

confidence: 99%

The Second Kummer Function with Matrix Parameters and Its Asymptotic Behaviour

Wehowar

Hausenblas

2018

Abstract and Applied Analysis

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“…Throughout this note C N×N will denote the complex space of all square complex matrices of common order N. For D ∈ C N×N the matrix version of the Pochhammer symbol (the shifted factorial) is defined in [1] in the form…”

Section: Introductionmentioning

confidence: 99%