Truncated Hermite polynomials

Dominici, Diego; Marcellán, Francisco

doi:10.48550/arxiv.2208.01125

Cited by 1 publication

(4 citation statements)

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“…and the result is immediate. □ Remark 4 Notice that for α = −1/2 you get (55) in [18]. It is a modified discrete Painlevé II equation (see [28,36]).…”

Section: Keeping This In Mindmentioning

confidence: 99%

“…□ Remark 3.7. The case where α " ´1{2 was studied by D. Dominici and F. Marcellán in [18]. Thus, hereinafter we shall deal with the case α ‰ ´1{2.…”

Section: Truncated Laguerre Linear Functional and The Symmetrization ...mentioning

confidence: 99%

“…On the other hand, in the particular case of two symmetric jumps, you get the so called Rys polynomials which play an important role in the evaluation of the electron repulsion integrals in quantum chemistry computer codes (see [32,37], among others). A connection with integrable systems in terms of a Toda perturbation of the Lebesque measure supported on r´1, 1s has been explored by many authors (see [18] and the updated list of references therein).…”

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confidence: 99%

“…If we define g n " γ n ´α 2 ´n 2 ´1 4 , then pg n q ně1 satisfies the following nonlinear recurrence relations. [18]. It is a modified discrete Painlevé II equation (see [28,36]).…”

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confidence: 99%

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Symmetrization process and truncated orthogonal polynomials

Dominici

García-Ardila

Marcellán

2023

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We define the family of truncated Laguerre polynomials Pn(x; z), orthogonal with respect to the linear functional ℓ defined by ⟨ℓ, p⟩ = z 0 p(x)x α e −x dx, α > −1. The connection between Pn(x; z) and the polynomials Sn(x; z) (obtained through the symmetrization process) constitutes a key element in our analysis. As a consequence, several properties of the polynomials Pn(x; z) and Sn(x; z) are studied taking into account the relation between the parameters of the three-term recurrence relations that they satisfy. Asymptotic expansions of these coefficients are given. Discrete Painlevé and Painlevé equations associated with such coefficients appear in a natural way. An electro-static interpretation of the zeros of such polynomials as well as the dynamics of the zeros in terms of the parameter z are given. MSC Classification: Primary: 42C05; 33C50

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“…and the result is immediate. □ Remark 4 Notice that for α = −1/2 you get (55) in [18]. It is a modified discrete Painlevé II equation (see [28,36]).…”

Section: Keeping This In Mindmentioning

confidence: 99%

“…□ Remark 3.7. The case where α " ´1{2 was studied by D. Dominici and F. Marcellán in [18]. Thus, hereinafter we shall deal with the case α ‰ ´1{2.…”

Section: Truncated Laguerre Linear Functional and The Symmetrization ...mentioning

confidence: 99%

mentioning

confidence: 99%

“…If we define g n " γ n ´α 2 ´n 2 ´1 4 , then pg n q ně1 satisfies the following nonlinear recurrence relations. [18]. It is a modified discrete Painlevé II equation (see [28,36]).…”

mentioning

confidence: 99%

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