Numerical computation of the Riemann zeta function and prime counting function by using Gauss-Hermite and Gauss-Laguerre quadratures

被引：1

作者：

Babolian, E. ^{[1
]}

Hajikandi, A. Arzhang ^{[1
]}

机构：

[1] Islamic Azad Univ, Sci & Res Branch, Dept Math, Tehran, Iran

来源：

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS | 2010年 / 87卷 / 15期

关键词：

Gauss-Laguerre quadrature; Gauss-Hermite quadrature; Riemann zeta function; prime counting function; prime numbers;

D O I：

10.1080/00207160903082371

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we transform (s) to appropriate integral forms and for numerical computing of these integrals, we introduce a method based on Gauss-Hermite and Gauss-Laguerre quadratures. By using the zeta function, we compute the prime counting function (x) numerically. Some relations are new and three examples are given to show the good accuracy of the method.

引用

页码：3420 / 3429

页数：10