Open AccessA central limit theorem for numbers satisfying a class of triangular arrays associated with Hermite polynomials
Author(s) -
Igoris Belovas
Publication year - 2021
Publication title -
lietuvos matematikos rinkinys
Language(s) - English
Resource type - Journals
eISSN - 2335-898X
pISSN - 0132-2818
DOI - 10.15388/lmr.2020.22466
Subject(s) - hermite polynomials , mathematics , limit (mathematics) , class (philosophy) , asymptotic distribution , limiting , normality , central limit theorem , orthogonal polynomials , generating function , convergence (economics) , function (biology) , pure mathematics , discrete mathematics , mathematical analysis , statistics , computer science , mechanical engineering , artificial intelligence , estimator , evolutionary biology , engineering , economics , biology , economic growth
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.