Central Limit Theorems for Combinatorial Numbers Associated with Laguerre Polynomials

Igoris Belovas
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Igoris Belovas: Faculty of Mathematics and Informatics, Institute of Data Science and Digital Technologies, Vilnius University, LT-04812 Vilnius, Lithuania

Mathematics, 2022, vol. 10, issue 6, 1-18

Abstract: In this paper, we study limit theorems for numbers satisfying a class of triangular arrays, which are defined by a bivariate linear recurrence with bivariate linear coefficients. We obtain analytical expressions for the semi-exponential generating function of several classes of the numbers, including combinatorial numbers associated with Laguerre polynomials. We apply these results to prove the numbers’ asymptotic normality and specify the convergence rate to the limiting distribution.

Keywords: limit theorems; combinatorial numbers; generating functions; asymptotic enumeration; asymptotic normality; Laguerre polynomials (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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