A Matrix Form of Ramanujan-type Series for 1/π

Abstract

In this paper we prove theorems related to the Ramanujan-type series for 1/π (type 3F2) and to the Ramanujan-like series, discovered by the author, for 1/π (type 5F4). Our developments for the cases 3F2 and 5F4 connect with the theory of modular functions and with the theory of CalabiYau differential equations, respectively.