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[Appeared in:
"Advances in Combinatorial Mathematics:
Proceedings of the Waterloo Workshop in Computer Algebra 2008
in honor of Georgy P. Egorychev", chapter 8, pp. 165174,
(I.Kotsireas, E.Zima, eds. Springer Verlag, 2009.)]
Written: Dec. 4, 2008.
Dedicated to Georgy Petrovich EGORYCHEV, on his 70th Birthday.
Back in the lateseventies and early eighties,
Georgy Egorychev built a very important bridge between the discrete and
the continuous, by reducing many
combinatorial sums and multisums to contour integrals and multiintegrals.
This is yet another bridge between the Discrete and the Continuous, this time
in Probability Theory.
Added Dec. 20, 2010: In May 2009 I gave a short talk about this work,
at the CANADAM 2009 conference, that has just been uploaded to YouTube.
Here is it is:
part1
part2
part3 .
Maple Packages
Important: This article is accompanied by Maple
packages
Sample Input and Output for CLT
To get a refined version of the Central Limit Theorem,
the input
gives the output.
Sample Input and Output for AsymptoticMoments

To get the aympototics for the moments of the Binomial Distribution,
the mahonian statistics (inversions on permutations) and the qCatalan distribution,
the input
gives the output.

To get the asymptotics of the even moments (the odd moments are zero) for rolling a fair kfaced die for k between 2 and 6,
the input
gives the output.

To get the asymptotics for the even moments (the odd moments are zero)
for plane partitions bounded in an n by n by k box for k between 1 and 4,
the input
gives the output.
Added March 27, 2009: Read Herb Wilf's
insightful comment
Added June 8, 2009: Georgy Petrovich EGORYCHEV invited me to
visit Krasnoyarsk, during May 1016, 2009,
and I had a great time, thanks to the
great hospitality of Georgy, his wife Zina, and his
amazing, computerwhiz, student, Maxim DAVLETSHIN.
Maxim took lots of
pictures
Thanks Maxim!
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