## Dixon's Theorem

 (1)
where is a Generalized Hypergeometric Function and is the Gamma Function. It can be derived from the Dougall-Ramanujan Identity. It can be written more symmetrically as

 (2)

where has a positive Real Part, , and . The identity can also be written as the beautiful symmetric sum
 (3)

(Petkovsek 1996).

References

Bailey, W. N. Generalised Hypergeometric Series. Cambridge, England: Cambridge University Press, 1935.

Cartier, P. and Foata, D. Problèmes combinatoires de commutation et réarrangements. New York: Springer-Verlag, 1969.

Knuth, D. E. The Art of Computer Programming, Vol. 1: Fundamental Algorithms, 2nd ed. Reading, MA: Addison-Wesley, 1973.

Petkovsek, M.; Wilf, H. S.; and Zeilberger, D. A=B. Wellesley, MA: A. K. Peters, p. 43, 1996.

Zeilberger, D. and Bressoud, D. A Proof of Andrew's -Dyson Conjecture.'' Disc. Math. 54, 201-224, 1985.