A Class of Conjectured Series Representations for 1/π

Abstract

Using the second conjecture in the paper [Guillera 06b] and inspired by the theory of modular functions, we find a method that allows us to obtain explicit formulas, involving eta or theta functions, for the parameters of a class of series for 1/π. As in [Guillera 06b], the series considered in this paper include Ramanujan's series as well as those associated with the Domb numbers and Apéry numbers.

Keywords:

• Primary 11F03
• Ramanujan series
• series for 1/π
• Domb numbers
• Apéry numbers
• Dedekind n function
• Jacobi θ functions