Jacobi matrix differential equation, polynomial solutions, and their properties

Defez, Emilio; Jódar, L.; Law, Anwesha

doi:10.1016/j.camwa.2004.01.011

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Introduction3

Extended Biorthogonal Matrix Polynomials1

Some Applications1

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Cited by 53 publications

(40 citation statements)

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“…For k = 1, formulas (2.7), (2.8) and (2.9) reduced to the wellknown matrix differential recurrence relations for Jacobi matrix polynomials in [8].…”

Section: Extended Biorthogonal Matrix Polynomialsmentioning

confidence: 99%

Extended biorthogonal matrix polynomials

Shehata¹

2017

Math Morav

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Abstract. The pair of biorthogonal matrix polynomials for commutative matrices were first introduced by Varma and Taşdelen in [22]. The main aim of this paper is to extend the properties of the pair of biorthogonal matrix polynomials of Varma and Tasdelen and certain generating matrix functions, finite series, some matrix recurrence relations, several important properties of matrix differential recurrence relations, biorthogonality relations and matrix differential equation for the pair of biorthogonal matrix polynomials J

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“…For k = 1, formulas (2.7), (2.8) and (2.9) reduced to the wellknown matrix differential recurrence relations for Jacobi matrix polynomials in [8].…”

Section: Extended Biorthogonal Matrix Polynomialsmentioning

confidence: 99%

Extended biorthogonal matrix polynomials

Shehata¹

2017

Math Morav

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“…the generating relation (2.4) can be written in the more compact form The Jacobi matrix polynomials P (A,B) n (x), n ∈ N, have been given in [7], for parameter matrices A and B whose eigenvalues µ satisfy (µ) > 0, as follows: …”

Section: Some Applicationsmentioning

confidence: 99%

Quasi-monomiality and operational identities for Laguerre–Konhauser-type matrix polynomials and their applications

Bin-Saad

Mohsen

2018

ACUTM

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Abstract. It is shown that an appropriate combination of methods, relevant to matrix polynomials and to operational calculus can be a very useful tool to establish and treat a new class of matrix LaguerreKonhauser polynomials. We explore the formal properties of the operational identities to derive a number of properties of the new class of Laguerre-Konhauser matrix polynomials and discuss the links with classical polynomials.

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“…In the recent work, matrix polynomials have significant emergent in [1]- [7], [9], [10], [12], [17]- [21], [24]- [32], [34]- [37]. Results in the theory of classical orthogonal polynomials have been extended to orthogonal matrix polynomials in [8], [16], [38].…”

Section: Introductionmentioning

confidence: 99%

Some relations on Humbert matrix polynomials

Shehata¹

2016

Math.Boh.

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Jacobi matrix differential equation, polynomial solutions, and their properties

Cited by 53 publications

References 12 publications

Extended biorthogonal matrix polynomials

Extended biorthogonal matrix polynomials

Quasi-monomiality and operational identities for Laguerre–Konhauser-type matrix polynomials and their applications

Some relations on Humbert matrix polynomials

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