q-Gauss Identity

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

			(2)
			(3)

where  is a q-binomial coefficient (Koepf 1998, p. 43).

REFERENCES:

Bhatnagar, G. Inverse Relations, Generalized Bibasic Series, and their U(n) Extensions. Ph.D. thesis. 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.