scholarly journals Multivariate Asymptotics for Products of Large Powers with Applications to Lagrange Inversion

10.37236/1440 ◽  
1999 ◽  
Vol 6 (1) ◽  
Author(s):  
Edward A. Bender ◽  
L. Bruce Richmond
Keyword(s):  
Limit Theorem ◽  
Generating Functions ◽  
Asymptotic Estimate ◽  
Local Limit Theorem ◽  
Local Limit ◽  
Combinatorial Enumeration ◽  
Lagrange Inversion ◽  
Enumeration Problems

An asymptotic estimate is given for the coefficients of products of large powers of generating functions. This theorem and another local limit theorem which is useful for conditioning are applied to various combinatorial enumeration problems that involve multivariate Lagrange inversion.

scholarly journals Central and Local Limit Theorems for Numbers of the Tribonacci Triangle

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 880
Author(s):  
Igoris Belovas
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Normal Distribution ◽  
Rate Of Convergence ◽  
Limit Theorems ◽  
Local Limit Theorem ◽  
Local Limit ◽  
Constructive Proof ◽  
The Central Limit Theorem ◽  
Local Limit Theorems

In this research, we continue studying limit theorems for combinatorial numbers satisfying a class of triangular arrays. Using the general results of Hwang and Bender, we obtain a constructive proof of the central limit theorem, specifying the rate of convergence to the limiting (normal) distribution, as well as a new proof of the local limit theorem for the numbers of the tribonacci triangle.

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