 
Summary: FASTER AND FASTER CONVERGENT SERIES FOR
3
Tewodros Amdeberhan
Department of Mathematics, Temple University, Philadelphia PA 19122, USA
tewodros@euclid.math.temple.edu
Submitted: April 8, 1996. Accepted: April 15, 1996
Abstract. Using WZ pairs we present accelerated series for computing
3
AMS Subject Classi cation: Primary 05A
Alf van der Poorten P gave a delightful account of Ap
ery's proof A of the irrationality of
3. Using
WZ forms, that came from WZ1 , Doron Zeilberger Z embedded it in a conceptual framework.
We recall Z that a discrete function An,k is called Hypergeometric or Closed Form CF in two
variables when the ratios An + 1;k=An;k and An;k + 1=An;k are both rational functions. A pair
F,G of CF functions is a WZ pair if Fn + 1;k , Fn;k = Gn;k + 1 , Gn;k. In this paper, after
choosing a particular F where its companion G is then produced by the amazing Maple package EKHAD
accompanying PWZ , we will give a list of accelerated series calculating
3. Our choice of F is
Fn;k = ,1kk!2sn ,k , 1!
sn +k +1!k +1
