Eisenstein Series, Alternative Modular Bases and Approximations of 1/π

2010/11/15 by Nikos Bagis, Bagis, Nikos
Mathematics · #11Y40 #11Y60 #33C75 #33E05 #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #General Mathematics (math.GM) #Mathematical functions and polynomials #math.GM #msc:11Y40 #msc:11Y60 #msc:33C75 #msc:33E05

paper · pdf · doi:10.48550/arxiv.1011.3496

Elliptic Functions; Pi

arxiv created 2010/11/15 · openalex publication_date 2010/11/15 · arxiv updated 2010/11/16 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

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 1/π formula. The result is a formula of 110 digits per term.

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