A central limit theorem for numbers satisfying a class of triangular arrays associated with Hermite polynomials - Belovas, Igoris (Lietuvos matematikos rinkinys, 2021)
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.
Keywords: limit theorems; combinatorial numbers; asymptotic enumeration; asymptotic normality; Hermite polynomials