Abstract :
I want to thank Ed Miller for the many useful insights he provided in his comments to my paper. I fully agree with him, summation-by-parts can be considered as yet another convergence-acceleration-method extrapolation technique. In my paper, the main purpose was to demonstrate the usefulness of summation by parts by using as an example the classic Leibniz-Gregory series for Pi. The resulting transformed series (that I called the ACE-2 series) was not supposed to be the "ultimate series for Pi", and I am grateful to Dr. Miller for mentioning the fascinating Ramanujan series, based on the modular function concept. Indeed, I have just found that the "ACE-2 series" was actually discovered and published as recently as in 1999 by Adamchik and Wagon, using a completely different approach. More on this will follow in a subsequent paper I hope to submit soon to this Magazine
