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 z_{0} is any point interior to C, then:

f(z_{0}) = 1/(2*pi**i*)*(the integral over C of)f(z)/(z - z_{0}) dz

From this it can be shownthat:

f^{(n)}(z_{0}) = (n!)/(2*pi**i*)*(the integral over C of)f(z)/((z - z_{0})^(n+1)) dz

where f^{(n)}(z_{0}) is the nth derivative of f(z_{0})