Complex series for 1/π

Many series for 1/π were discovered since the appearance of S. Ramanujan’s famous paper “Modular equations and approximation to π” published in 1914. Almost all these series involve only real numbers. Recently, in an attempt to prove a series for 1/π discovered by Z.-W. Sun, the authors found that a series for 1/π involving complex numbers is needed. In this article, we illustrate a method that would allow us to prove series of this type.