Some Remarks on a recent article by J. -P. Allouche

by Shalosh B. Ekhad and Doron Zeilberger

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Written: Purim 5779 (aka March 22, 2019)

We doubt whether the American Mathematical Monthly would publish an article entitled "A new proof that 123*321= 39483",
but it sure does publish papers of equally routinely verifiable identities.

In 1980 Otto G. Ruehr made some puzzling comments that a certain identity A, that he proved, is equivalent to another identity B, but he did not explain why they are equivalent. Recently J.-P. Allouche tried to explain why they are "equivalent", using about eight pages. We comment that it is extremely unlikely to be Ruehr's reasoning (he probably got mixed up with a different problem), but be that as it may, it is not worthwhile to try and deduce B from A, since both A and B are routinely provable using Wilf-Zeilberger algorithmic proof theory (implemented in Maple) and the Almkvist-Zeilberger algorithm.

Added March 25, 2019: Read Dr. Z.'s Opininion 170 and Jean-Paul Allouche's interesting response

Added May 18, 2019: Read Christian Krattenthaler's interesting comments

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