A central limit theorem for numbers satisfying a class of triangular arrays associated with Hermite polynomials

A central limit theorem for numbers satisfying a class of triangular arrays associated with Hermite polynomials

The paper extends the investigations of limit theorems for numbers satisfying a class of triangular arrays. We obtain analytical expressions for the semiexponential generating function the numbers, associated with Hermite polynomials. We apply the results to prove the asymptotic normality of the nu...

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Bibliographic Details
Main Author: Igoris Belovas
Format: Article
Language:English
Published: Vilnius University Press 2021-03-01
Series:Lietuvos Matematikos Rinkinys
Subjects:
limit theorems
combinatorial numbers
asymptotic enumeration
asymptotic normality
Hermite polynomials
Online Access:https://www.zurnalai.vu.lt/LMR/article/view/22466
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spelling doaj-1e731a6fb107402b9d42a2f8045256a92021-03-16T09:22:46ZengVilnius University PressLietuvos Matematikos Rinkinys0132-28182335-898X2021-03-0161B10.15388/LMR.2020.22466A central limit theorem for numbers satisfying a class of triangular arrays associated with Hermite polynomialsIgoris Belovas0 Vilnius University, Vilnius Gediminas Technical University The paper extends the investigations of limit theorems for numbers satisfying a class of triangular arrays. We obtain analytical expressions for the semiexponential generating function the numbers, associated with Hermite polynomials. We apply the results to prove the asymptotic normality of the numbers and specify the convergence rate to the limiting distribution.    https://www.zurnalai.vu.lt/LMR/article/view/22466limit theoremscombinatorial numbersasymptotic enumerationasymptotic normalityHermite polynomials
collection DOAJ
language English
format Article
sources DOAJ
author Igoris Belovas
spellingShingle Igoris Belovas
A central limit theorem for numbers satisfying a class of triangular arrays associated with Hermite polynomials
Lietuvos Matematikos Rinkinys
limit theorems
combinatorial numbers
asymptotic enumeration
asymptotic normality
Hermite polynomials
author_facet Igoris Belovas
author_sort Igoris Belovas
title A central limit theorem for numbers satisfying a class of triangular arrays associated with Hermite polynomials
title_short A central limit theorem for numbers satisfying a class of triangular arrays associated with Hermite polynomials
title_full A central limit theorem for numbers satisfying a class of triangular arrays associated with Hermite polynomials
title_fullStr A central limit theorem for numbers satisfying a class of triangular arrays associated with Hermite polynomials
title_full_unstemmed A central limit theorem for numbers satisfying a class of triangular arrays associated with Hermite polynomials
title_sort central limit theorem for numbers satisfying a class of triangular arrays associated with hermite polynomials
publisher Vilnius University Press
series Lietuvos Matematikos Rinkinys
issn 0132-2818
2335-898X
publishDate 2021-03-01
description The paper extends the investigations of limit theorems for numbers satisfying a class of triangular arrays. We obtain analytical expressions for the semiexponential generating function the numbers, associated with Hermite polynomials. We apply the results to prove the asymptotic normality of the numbers and specify the convergence rate to the limiting distribution.    
topic limit theorems
combinatorial numbers
asymptotic enumeration
asymptotic normality
Hermite polynomials
url https://www.zurnalai.vu.lt/LMR/article/view/22466
work_keys_str_mv AT igorisbelovas acentrallimittheoremfornumberssatisfyingaclassoftriangulararraysassociatedwithhermitepolynomials
AT igorisbelovas centrallimittheoremfornumberssatisfyingaclassoftriangulararraysassociatedwithhermitepolynomials
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