The 
-Dougall sum is Jackson's q-analog
of Dougall's theorem (Jackson 1921). It is the
identity
![_8phi_7[a,qa^(1/2),-qa^(1/2),b,c,d,e,q^(-N); a^(1/2),-a^(1/2),(aq)/b,(aq)/c,(aq)/d,(aq)/e,aq^(N+1);q,q]=(((aq)/(bd);q)_N((aq)/(cd);q)_N(aq;q)_N((aq)/(bc);q)_N)/(((aq)/d;q)_N((aq)/(bcd);q)_N((aq)/b;q)_N((aq)/c;q)_N),](/images/equations/q-DougallSum/NumberedEquation1.svg) |
where 
and 
is a q-hypergeometric
function.
q-Dougall Sum
See also
Dougall's Theorem, q-AnalogExplore with Wolfram|Alpha
References
Bhatnagar, G. "Inverse Relations, Generalized Bibasic Series, and Their
Extensions." PhD thesis. Columbus, OH: Ohio State University, p. 36, 1995.Gasper,
G. and Rahman, M. Basic
Hypergeometric Series. Cambridge, England: Cambridge University Press, p. 35,
1990.Jackson, F. H. "Summation of 
-Hypergeometric Series." Messenger Math. 50,
101-112, 1921.Referenced on Wolfram|Alpha
q-Dougall SumCite this as:
Weisstein, Eric W. "q-Dougall Sum." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/q-DougallSum.html