q-Apery Irrationality Proofs by q-WZ Pairs

by Tewodros Amdeberhan and Doron Zeilberger

.pdf   .ps   .tex

(Adv. Appl. Math. 20(1998), 275-283.).

Written: Sept. 12, 1996.

We all know the heartwarming story of how the `little guy', Roger Apery, suddenly became a celebrity at the age of 64, when he proved that Zeta(3) is irrational. As usual, such fairytales are not quite accurate. In a fascinating account by his son, Francois, in a recent Math. Intell. issue, we find that Roger Apery was not at all `litte' when he was young, but a real hotshot. Then he became more interested in politics than in publishing, until his amazing tour-de-force.

I am sure that Apery's ideas will lead to much more, with or without WZ pairs and forms. In this paper we make a modest start by q-analogizing Apery's irrationality proof of log(2), using the q-analog of WZ pairs, as well as applying it to the `q-Harmonic series'.

Tewodros Amdeberhan prepared a small Web Page with supporting data

Added Dec. 8, 1998: Laurent Habsieger has sent us the following interesting message.

Doron Zeilberger's List of Papers

Doron Zeilberger's Home Page