Searching for Apery-Style Miracles [Using, Inter-Alia, the Amazing Almkvist-Zeilberger Algorithm]
arXiv:1405.4445
Abstract
Roger Apery's seminal method for proving irrationality is "turned on its head" and taught to computers, enabling a one second redux of the original proof of zeta(3), and many new irrationality proofs of many new constants, alas, none of them is both famous and not-yet-proved-irrational.
16 pages. Exclusively published in the Personal Journal of Shalosh B. Ekhad and Doron Zeilberger, May 2014, and this arxiv.org. Accompanied my Maple package NesApery, available from http://www.math.rutgers.edu/~zeilberg/tokhniot/NesApery