Jackson's Identity

A q-Series identity involving

$${(aq)_q^m (aqde)_q^m (adec)_q^m (aqcd)_q^m \over (aqc)_q^m(aqd)_q^m(aqe)_q^m(aqcde)_q^m},$$

where

$$(a)_q^n = (1-a)(1-aq)\cdots(1-aq^{n-1}).$$

See also q-Series

References

Hardy, G. H. Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work, 3rd ed. New York: Chelsea, pp. 109-110, 1959.

Jackson, F. H. ``Summation of $q$-Hypergeometric Series.'' Messenger Math. 47, 101-112, 1917.