based on a problem in particle physics. The theorem is called Dyson's conjecture, and was proved by Wilson (1962) and independently by Gunson (1962).
A definitive proof was subsequently published by Good (1970).

A -analog
of this theorem (Andrews 1975) states that the coefficient of in

(3)

where

(4)

is given by

(5)

This can also be stated in the form that the constant term of

Andrews, G. E. "Problems and Prospects for Basic Hypergeometric Functions." In The
Theory and Application of Special Functions (Ed. R. Askey). New York:
Academic Press, pp. 191-224, 1975.Andrews, G. E. "The
Zeilberger-Bressoud Theorem." §4.3 in q-Series:
Their Development and Application in Analysis, Number Theory, Combinatorics, Physics,
and Computer Algebra. Providence, RI: Amer. Math. Soc., pp. 36-38, 1986.Dyson,
F. "Statistical Theory of the Energy Levels of Complex Systems. I." J.
Math. Phys.3, 140-156, 1962a.Dyson, F. "Statistical
Theory of the Energy Levels of Complex Systems. II." J. Math. Phys.3,
157-165, 1962b.Dyson, F. "Statistical Theory of the Energy Levels
of Complex Systems. III." J. Math. Phys.3, 166-175, 1962c.Good,
I. J. "Short Proof of a Conjecture by Dyson." J. Math. Phys.11,
1884, 1970.Gunson, J. "Proof of a Conjecture of Dyson in the Statistical
Theory of Energy Levels." J. Math. Phys.3, 752-753, 1962.Wilson,
K. G. "Proof of a Conjecture by Dyson." J. Math. Phys.3,
1040-1043, 1962.Zeilberger, D. and Bressoud, D. M. "A Proof
of Andrews' -Dyson
Conjecture." Disc. Math.54, 201-224, 1985.