A formula first derived by Augustin Cauchy.

Given f is a complex function which is analytic within and on a positively oriented simple closed contour C, and z0 is any point interior to C, then:

f(z0) = 1/(2*pi*i)*(the integral over C of)f(z)/(z - z0) dz

From this it can be shownthat:

f(n)(z0) = (n!)/(2*pi*i)*(the integral over C of)f(z)/((z - z0)^(n+1)) dz

where f(n)(z0) is the nth derivative of f(z0)