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q-Chu-Vandermonde Identity

A q-analog of the Chu-Vandermonde identity given by

_2phi_1(q^(-n),b;c;q,cq^n/b)=((cq^n;q)_infty(c/b;q)_infty)/((c;q)_infty(cq^n/b;q)_infty)=((c/b;q)_n)/((c;q)_n),

where _2phi_1(a,b;c;q,z) is the q-hypergeometric function. The identity can also be written as

_2phi_1(q^(-n),b;c;q,q)=((c/b;q)_n)/((c;q)_n)b^n.

See also

Chu-Vandermonde Identity, q-Hypergeometric Function

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References

Bhatnagar, G. Inverse Relations, Generalized Bibasic Series, and their U(n) Extensions. Ph.D. thesis. Ohio State University, p. 18, 1995.Gasper, G. and Rahman, M. Basic Hypergeometric Series. Cambridge, England: Cambridge University Press, p. 236, 1990.Koepf, W. Hypergeometric Summation: An Algorithmic Approach to Summation and Special Function Identities. Braunschweig, Germany: Vieweg, p. 43, 1998.

Referenced on Wolfram|Alpha

q-Chu-Vandermonde Identity

Cite this as:

Weisstein, Eric W. "q-Chu-Vandermonde Identity." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/q-Chu-VandermondeIdentity.html

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