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The 
-Gauss
identity is a q-analog of Gauss's theorem due
to Jacobi and Heine,
 |
(1)
|
for 
(Gordon and McIntosh 1997; Koepf 1998, p. 40), where 
is a q-hypergeometric
function. A special case for 
is given by
![sum_(k=0)^(n)q^(k^2)[n; k]_q^2](/images/equations/q-GaussIdentity/Inline5.svg) |  |  |
(2)
|
 |  |  |
(3)
|
where ![[n; k]_q](/images/equations/q-GaussIdentity/Inline11.svg)
is a q-binomial coefficient (Koepf
1998, p. 43).
Extensions." PhD thesis. Columbus, OH: Ohio State University, p. 31, 1995.Gasper,
G. and Rahman, M. Basic
Hypergeometric Series. Cambridge, England: Cambridge University Press, pp. 10
and 236, 1990.Gordon, B. and McIntosh, R. J. "Algebraic Dilogarithm
Identities." Ramanujan J. 1, 431-448, 1997.Koepf,
W. Hypergeometric
Summation: An Algorithmic Approach to Summation and Special Function Identities.
Braunschweig, Germany: Vieweg, 1998.Weisstein, Eric W. "q-Gauss Identity." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/q-GaussIdentity.html
