Decomposition of some Hankel matrices generated by the generalized rencontres polynomials

Ferrari, Margherita Maria; Munarini, Emanuele

doi:10.1016/j.laa.2018.12.029

Cited by 3 publications

(4 citation statements)

References 18 publications

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“…We will prove that the matrix H (ν) (x) = H (ν;0) (x) admits a Sheffer LDU-factorization, while the matrix H (ν;1) (x) admits a Sheffer LTUfactorization. More precisely, an infinite matrix A has a Sheffer LDU-factorization [40] when there exist two Sheffer matrices S 1 and S 2 with main diagonal 1 and a diagonal matrix…”

Section: Hankel Matricesmentioning

confidence: 99%

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Tricomi Continuants

Munarini

2024

Mathematics

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In this paper, we introduce and study the Tricomi continuants, a family of tridiagonal determinants forming a Sheffer sequence closely related to the Tricomi polynomials and the Laguerre polynomials. Specifically, we obtain the main umbral operators associated with these continuants and establish some of their basic relations. Then, we obtain a Turan-like inequality, some congruences, some binomial identities (including a Carlitz-like identity), and some relations with the Cayley continuants. Furthermore, we show that the infinite Hankel matrix generated by the Tricomi continuants has an LDU-Sheffer factorization, while the infinite Hankel matrix generated by the shifted Tricomi continuants has an LTU-Sheffer factorization. Finally, by the first factorization, we obtain the linearization formula for the Tricomi continuants and its inverse.

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Section: Hankel Matricesmentioning

confidence: 99%

“…Similarly, an infinite matrix A has a Sheffer LTU-factorization [40] when there exist two Sheffer matrices S 1 and S 2 with main diagonal 1 and a tridiagonal matrix T such that A = S 1 TS T 2 . To obtain these factorizations, we will use the exponential generating series of the infinite matrices H (ν) (x) and H (ν;1) (x).…”

Section: Hankel Matricesmentioning

confidence: 99%

Tricomi Continuants

Munarini

2024

Mathematics

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“…These sequences appear in various contexts, such as applied mathematics, physics, geometric probability, interpolation of functions, number theory, umbral calculus and combinatorics. They include several classical polynomials and possess numerous algebraic, analytic and combinatorial properties [2,18,20,21] (see also [13,14,15,3,9]). Furthermore, several Sheffer polynomials can be expressed in terms of the Cayley continuants or the generalized Sylvester continuants, such as the Meixner polynomials of the first kind, the Mittag-Leffler polynomials, the Pidduck polynomials and the central factorial polynomials.…”

Section: Introductionmentioning

confidence: 99%

Umbral operators for Cayley and Sylvester continuants

Munarini

2022

APPL ANAL DISCRETE M

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We study the main umbral operators J, M and N associated with the Cayley continuants U(?)n(x) and the generalized Sylvester continuants H(?)n(x) = U(?+n)n(x). In particular, we obtain their representation in terms of the differential operator Dx and the shift operator E. Then, by using these representations, we obtain some combinatorial and differential identities for the continuants U(?)n(x) and H(?)n(x).

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“…Generalized rencontres polynomials. Let m ∈ N. The generalized rencontres polynomials D (m) n (x), the generalized permutation polynomials P (m) n (x) and the generalized arrangement polynomials A (m) n (x) are defined by (see [3,5])…”

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An Operational Approach to the Generalized Rencontres Polynomials

MUNARINI¹

2022

KgJMat

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In this paper, we study the umbral operators J, M and N associated with the generalized rencontres polynomials D(m) n (x). We obtain their representations in terms of the differential operator Dx and the shift operator E. Then, by using these representations, we obtain some combinatorial and differential identities for the generalized rencontres polynomials. Finally, we extend these results to some related polynomials and, in particular, to the generalized permutation polynomials P(m)n (x) and the generalized arrangement polynomials A(m)n (x).

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Decomposition of some Hankel matrices generated by the generalized rencontres polynomials

Cited by 3 publications

References 18 publications

Tricomi Continuants

Tricomi Continuants

Umbral operators for Cayley and Sylvester continuants

An Operational Approach to the Generalized Rencontres Polynomials

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