A General Method for Constructing Ramanujan Formulas for 1/π^ν

2012/07/07 by Bagis, Nikos
#11Y60 #33C05 #33C75 #33E05 #FOS: Mathematics #General Mathematics (math.GM)

paper · doi:10.48550/arxiv.1208.4567

Abstract

In this article we give the theoretical background for generating Ramanujan type 1/π^2ν formulas. As applications of our method we give a general construction of 1/π⁴ series and examples of 1/π⁶ series. We also study the elliptic alpha function whose values are useful for such evaluations.

Related

• A family of Ramanujan-Orr formulas for 1/π
• A method for proving Ramanujan series for 1/π
• Proofs of some Ramanujan series for 1/π using a Zeilberger's program
• Ramanujan type 1/π Approximation Formulas
• On proving some of Ramanujan's formulas for \frac1π with an elementary method