Conjectures on the evaluation of alternative modular bases and formulas approximating 1/π

被引：3

作者：

Bagis, N. D. ^{[1
]}

Glasser, M. L. ^{[2
]}

机构：

[1] Aristotle Univ Thessaloniki, Dept Informat, Thessaloniki, Greece

[2] Clarkson Univ, Dept Phys, Potsdam, NY 13699 USA

来源：

JOURNAL OF NUMBER THEORY | 2012年 / 132卷 / 10期

关键词：

Elliptic functions; Singular modulus; Ramanujan's cubic theory; Pi; RAMANUJANS SERIES;

D O I：

10.1016/j.jnt.2012.04.010

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article using the theory of Eisenstein series, we give the complete evaluation of two Gauss hypergeometric functions. Moreover we evaluate the modulus of each of these functions and the values of the functions in terms of the complete elliptic integral of the first kind K. As application we give way of how to evaluate the parameters in a closed-well posed form, of a general Ramanujan type 1/pi formula. The result is a formula of 110 digits per term. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：2353 / 2370

页数：18