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)