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math.NT2021
Experimenting with Apery Limits and WZ pairs
Robert Dougherty-Bliss, Doron Zeilberger
This article, dedicated with admiration in memory of Jon and Peter Borwein, illustrates by example, the power of experimental mathematics, so dear to them both, by experimenting wi…
math.HO2021
Integral Recurrences from A to Z
Robert Dougherty-Bliss
George Boros and Victor Moll's masterpiece "Irresistible Integrals" does well to include a suitably-titled appendix, "The Revolutionary WZ Method," which gives a brief overview of…
math.NT2021
Tweaking the Beukers Integrals In Search of More Miraculous Irrationality Proofs A La Apery
Robert Dougherty-Bliss, Christoph Koutschan, Doron Zeilberger
There are only aleph-zero rational numbers, while there are 2 to the power aleph-zero real numbers. Hence the probability that a randomly chosen real number would be rational is 0.…