Eisenstein Series, Alternative Modular Bases and Approximations of $1/\pi$
General Mathematics
2010-11-16 v1
Abstract
In this article using the theory of Eisenstein series, we give rise to 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. As application we give way of how to evaluate the parameters, in a closed-well posed form, of a general Ramanujan type formula. The result is a formula of 110 digits per term.
Keywords
Cite
@article{arxiv.1011.3496,
title = {Eisenstein Series, Alternative Modular Bases and Approximations of $1/\pi$},
author = {Nikos Bagis},
journal= {arXiv preprint arXiv:1011.3496},
year = {2010}
}
Comments
Elliptic Functions; Pi