q-Vandermonde Sum

$${}_2\phi_1(a,q^{-n};c;q,q)={a^n(c/a,q)_n\over(c;q)_n},$$

where ${}_2\phi_1(a,b;c;q,z)$ is a Heine Hypergeometric Series.

See also Chu-Vandermonde Identity, Heine Hypergeometric Series

References

Andrews, G. E. $q$-Series: Their Development and Application in Analysis, Number Theory, Combinatorics, Physics, and Computer Algebra. Providence, RI: Amer. Math. Soc., pp. 15-16, 1986.