New Generalizations of Two Ramanujan Series for $1/\pi$

Abstract

By utilizing two hypergeometric summation identities we extend two well-known Ramanujan series for $1/\pi$ by making each of them a member of an infinite family of series. We also find the corresponding families involving harmonic numbers and odd harmonic numbers.To further illustrate our method we derive families of Ramanujan-like series associated with a hypergeometric series derived by Lavoie and two hypergeometric series from Bailey's book.

18 pages, no figures or tables