The q-hypergeometric function identity
![_rphi_s^'[a,qsqrt(a),-qsqrt(a),1/b,1/c,1/d,1/e,1/f; sqrt(a),-sqrt(a),abq,acq,adq,aeq,afq]
=((aq)_q^m(aqde)_q^m(adec)_q^m(aqcd)_q^m)/((aqc)_q^m(aqd)_q^m(aqe)_q^m(aqcde)_q^m),](/images/equations/JacksonsIdentity/NumberedEquation1.svg) |
where
 |
is a q-hypergeometric
function, and one of 
, 
, 
, 
, or 
is equal to 
(Hardy 1999, pp. 108-109). This identity includes the
Dougall-Ramanujan identity as a special
case.
Jackson's Identity
See also
Dougall-Ramanujan Identity, Jackson-Slater Identity, q-Hypergeometric FunctionExplore with Wolfram|Alpha
References
Bailey, W. N. Generalised Hypergeometric Series. Cambridge, England: Cambridge University Press, pp. 66-72, 1935.Hardy, G. H. Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work, 3rd ed. New York: Chelsea, pp. 109-110, 1999.Jackson, F. H. "Summation of
-Hypergeometric
Series." Messenger Math. 50, 101-112, 1921.Referenced on Wolfram|Alpha
Jackson's IdentityCite this as:
Weisstein, Eric W. "Jackson's Identity." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/JacksonsIdentity.html