A 
-analog
of the Saalschütz theorem due to Jackson is given by
 |
where 
is the q-hypergeometric function
(Koepf 1998, p. 40; Schilling and Warnaar 1999).
q-Saalschütz Sum
See also
q-Hypergeometric FunctionExplore with Wolfram|Alpha
References
Andrews, G. E. Encyclopedia of Mathematics and Its Applications, Vol. 2: The Theory of Partitions. Cambridge, England: Cambridge University Press, 1984.Bailey, W. N. "The Analogue of Saalschütz's Theorem." §8.4 in Generalised Hypergeometric Series. Cambridge, England: University Press, p. 68, 1935.Bhatnagar, G. Inverse Relations, Generalized Bibasic Series, and their U(n) Extensions. Ph.D. thesis. Ohio State University, p. 30, 1995.Carlitz, L. "Remark on a Combinatorial Identity." J. Combin. Th. Ser. A 17, 256-257, 1974.Gasper, G. and Rahman, M. Basic Hypergeometric Series. Cambridge, England: Cambridge University Press, p. 13, 1990.Gould, H. W. "A New Symmetrical Combinatorial Identity." J. Combin. Th. Ser. A 13, 278-286, 1972.Koepf, W. Hypergeometric Summation: An Algorithmic Approach to Summation and Special Function Identities. Braunschweig, Germany: Vieweg, pp. 25-26, 1998.Schilling A. and Warnaar, S. O. "A Generalization of the q.-Saalschütz Sum and the Burge Transform" 8 Sep 1999. http://arxiv.org/abs/math.QA/9909044.Watson, G. N. "A New Proof of the Rogers-Ramanujan Identities." J. London Math. Soc. 4, 4-9, 1929.Referenced on Wolfram|Alpha
q-Saalschütz SumCite this as:
Weisstein, Eric W. "q-Saalschütz Sum." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/q-SaalschuetzSum.html