q-Gauss Identity
المؤلف:
Bhatnagar, G.
المصدر:
Inverse Relations, Generalized Bibasic Series, and their U(n) Extensions. Ph.D. thesis. Ohio State University
الجزء والصفحة:
...
28-8-2019
1862
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
where ![[n; k]_q](http://mathworld.wolfram.com/images/equations/q-GaussIdentity/Inline10.gif)
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.
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