Abstract
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.
 
Highlights
Limit theorems for numbers satisfying a class of triangular arrays
A central limit theorem for numbers satisfying a class of triangular arrays
We apply the results to prove the asymptotic normality of the numbers and specify the convergence rate to the limiting distribution
Summary
Straipsnyje yra nagrinėjamas dalinis trikampių masyvų klasės skaičių [3] atvejis. Trikampių masyvų klasės skaičiai apibrėžiami rekurentiniu sąryšiu ank = f1(n, k)an−1,k−1 + f2(n, k)an−1,k,. Kur a00 = 1 ir ank = 0, kai min(n − k, n, k) < 0. Darbe [1] buvo išvesta (1) skaičių su tiesiniais koeficientais f1(n, k) = k11n + k12k + k13, f2(n, k) = k21n + k22k + k23, kij ∈ R, (2). Generuojančios funkcijos bendroji dalinių išvestinių diferencialinė lygtis
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