.pdf .ps .tex

Written: July 10, 2014

[Exclusively published in the Personal Journal of Shalosh B. Ekhad and Doron Zeilberger and arxiv.org]

Dedicated to Dick Askey (b. June 4, 1933), from a 4

Added July 14, 2014: Jang Soo Kim independently found a proof, that is complete (not just a sketch), with all the steps rigorously justified!

In 1998, Clara S. Chan, David P. Robbins, and David S. Yuen conjectured and I proved, using the amazing Morris Constant Term Identity (that may be viewed as a contour-integral analog of the Selberg integral).

Recently Karola Mészáros and Alejandro Morales,
conjectured a D_{n} analog of the
Chan-Robbins-Yuen formula, getting another constant-term expression.
This conjecture was also mentioned by Alejandro Morales in the
Open Problems session that took place on June 23, 2014, ca. 4:50-5:00pm at the
Stanley@70 conference
[see his gorgeous slides].

It turns out that the Mészáros-Morales conjecture is a special case of a much more general constant term identity, and the proof in the present article is a "cheating" proof for two reasons:

- it uses analysis ,
- it has some handwaving, and I have an annoying sign still lingering ,

Let me also comment that for any fixed dimension n, the new constant term identity is doable by the WZ method, and I am also sure that one can get a completely elementary WZ-style proof for general dimensions, by looking at the output for small n, and finding a pattern, like it was done for the original Selberg integral in section 6.5 of this masterpiece.

Personal Journal of Shalosh B. Ekhad and Doron Zeilberger