Central Limit Theorems for Combinatorial Numbers Associated with Laguerre Polynomials
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, includin...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-03-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/6/865 |
| _version_ | 1797445495572922368 |
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| author | Igoris Belovas |
| author_facet | Igoris Belovas |
| author_sort | Igoris Belovas |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-09T13:26:37Z |
| format | Article |
| id | doaj.art-cab3d70b7b0b43dba9f616ef4e5daed9 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T13:26:37Z |
| publishDate | 2022-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-cab3d70b7b0b43dba9f616ef4e5daed92023-11-30T21:23:16ZengMDPI AGMathematics2227-73902022-03-0110686510.3390/math10060865Central Limit Theorems for Combinatorial Numbers Associated with Laguerre PolynomialsIgoris Belovas0Faculty of Mathematics and Informatics, Institute of Data Science and Digital Technologies, Vilnius University, LT-04812 Vilnius, LithuaniaIn 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.https://www.mdpi.com/2227-7390/10/6/865limit theoremscombinatorial numbersgenerating functionsasymptotic enumerationasymptotic normalityLaguerre polynomials |
| spellingShingle | Igoris Belovas Central Limit Theorems for Combinatorial Numbers Associated with Laguerre Polynomials Mathematics limit theorems combinatorial numbers generating functions asymptotic enumeration asymptotic normality Laguerre polynomials |
| title | Central Limit Theorems for Combinatorial Numbers Associated with Laguerre Polynomials |
| title_full | Central Limit Theorems for Combinatorial Numbers Associated with Laguerre Polynomials |
| title_fullStr | Central Limit Theorems for Combinatorial Numbers Associated with Laguerre Polynomials |
| title_full_unstemmed | Central Limit Theorems for Combinatorial Numbers Associated with Laguerre Polynomials |
| title_short | Central Limit Theorems for Combinatorial Numbers Associated with Laguerre Polynomials |
| title_sort | central limit theorems for combinatorial numbers associated with laguerre polynomials |
| topic | limit theorems combinatorial numbers generating functions asymptotic enumeration asymptotic normality Laguerre polynomials |
| url | https://www.mdpi.com/2227-7390/10/6/865 |
| work_keys_str_mv | AT igorisbelovas centrallimittheoremsforcombinatorialnumbersassociatedwithlaguerrepolynomials |