A Local Limit Theorem for the Distribution of Fractional Parts of an Exponential Function

1979 ◽  
Vol 23 (3) ◽  
pp. 521-528 ◽  
Author(s):  
D. A. Moskvin ◽  
A. G. Postnikov
Keyword(s):  
Limit Theorem ◽  
Exponential Function ◽  
Local Limit Theorem ◽  
Local Limit

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.

scholarly journals Local limit theorem for coefficients of modified Borwein’s algorithm, proved by the ratio method

2019 ◽  
Vol 60 ◽  
pp. 11-14
Author(s):  
Igoris Belovas
Keyword(s):  
Limit Theorem ◽  
Zeta Function ◽  
Riemann Zeta Function ◽  
Local Limit Theorem ◽  
Local Limit ◽  
Ratio Method ◽  
The Riemann Zeta Function ◽  
Riemann Zeta

The paper continues the research of the modified Borwein method for the evaluation of the Riemann zeta-function. It provides a different perspective on the derivation of the local limit theorem for coefficients of the method. The approach is based on the ratio method, proposed by Proschan.  

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