A General Method for Constructing Ramanujan Formulas for $1/{\pi }^{\nu }$

Abstract

In this article we give the theoretical background for generating Ramanujan type $1/{\pi }^{2\nu }$ formulas. As applications of our method we give a general construction of $1/{\pi }^4$ series and examples of $1/{\pi }^6$ series. We also study the elliptic alpha function whose values are useful for such evaluations.

pi formulas, Ramanujan, 12 pages