January 6th, 2012, 9:25 pm
If df/dz exists at some point z0, then f(z) is analytic in some neighborhood of z0. Suppose C is any closed curve in that neighborhood,enclosing z0. The curve might be quite far from z0. Then, an interesting thing about analytic functions is that you could get thederivative by doing an integration which only uses the values of the function _away_ from the point of interest:For example, you could integrate around a square surrounding z_0.Or, if the function falls off fast enough, you could integrate along the entire real axis, since the contribution from the rest of contour will vanish.Efficient way to get the derivative? Not at all -- just interesting
Last edited by
Alan on January 5th, 2012, 11:00 pm, edited 1 time in total.