Vandermonde Theorem

A special case of Gauss's Theorem with $a$ a Negative Integer $-n$:

$${}_2F_1(-n,b;c;1) = {(c-b)_n\over (c)_n},$$

where ${}_2F_1(a,b;c;z)$ is a Hypergeometric Function and $(a)_n$ is a Pochhammer Symbol (Bailey 1935, p. 3).

See also Gauss's Theorem

References

Bailey, W. N. Generalised Hypergeometric Series. Cambridge, England: Cambridge University Press, 1935.