ABSTRACT
In 2002 and 2006, using a Wilf–Zeilberger-based method, Guillera introduced proofs for evaluations for what are considered as the simplest two series out of Ramanujan's 17 series for . In this article, we show how the WZ method may be used in a fundamentally and nontrivially different way to prove these results, and to obtain identities for infinite families of Ramanujan-like series for
. We introduce a
-recurrence that we had discovered experimentally, and we prove this recursion using the WZ method and apply it to obtain a series acceleration formula that we apply to formulate a new and simple proof for the Ramanujan series for
that has a convergence rate of
, and we provide an infinite family of generalizations of this formula, and similarly for Ramanujan's series of convergence rate
.
MATHEMATICS SUBJECT CLASSIFICATION:
Disclosure statement
No potential conflict of interest was reported by the author(s).