A central limit theorem for coefficients of the modified Borwein method for the calculation of the Riemann zeta-function

Central and Local Limit Theorems for Numbers of the Tribonacci Triangle

“…The present research extends the investigations of the asymptotics for Delannoy numbers undertaken by Noble [9,10] and Wang, Zheng and Chen [11] (as well as our research into central and local limit theorems for combinatorial numbers satisfying a class of triangular arrays [12][13][14][15]). Noble has obtained asymptotic expansions for the central weighted Delannoy numbers (u r,r ) and the numbers along the the diagonal with slope 2 (u r,2r ).…”

A local limit theorem for coefficients of modified Borwein's method

“…Remark 2.4. A central limit theorem for the coefficients of modified Borwein's method can be proved analogically, using Bender's central limit theorem applied to asymptotic enumeration (Theorem 1, [2,3]. However, the approach, based on Hwang's limit theorem ( [5]), yields stronger result, enabling us to evaluate the rate of convergence to normal distribution (cf.…”

Series with Binomial-Like Coefficients for Evaluation and 3D Visualization of Zeta Functions

“…Borwein et al, 2000;Borwein, 2000). Belovas obtained central (Belovas, 2019a) and local (Belovas, 2019b) limit theorems, which allowed to introduce an asymptotic approximation for coefficients of the algorithm, providing a considerable speedup in calculations (Belovas and Sakalauskas, 2018).…”