Some comprehensive expressions for π and 1/π

Abstract

Comprehensive expressions for numerous series involving π and 1/π are given. These include series which begin with an even or odd truncation of the products in Wallis's [5] expression, and bind π or 1/π from below or above. The series considered previously [1, 2] are shown to be special cases of these expressions.

Keywords:

• Monotonic series
• truncation
• convergence
• harmonic oscillator functions