A New Method to Obtain Series for 1/π and 1/π²

Abstract

We give several conjectures that allow us to derive many series for 1/π and 1/π². These series include Ramanujan's series, as well as those associated with the Domb numbers and Apéry numbers. We have checked the conjectures numerically in many examples with a precision of two hundred digits.

Keywords:

• 33C20
• Ramanujan series
• series for 1/π
• series for 1/π²
• Domb numbers
• Apéry numbers