An anti-analytic function is a function f satisfying the condition (d f)/(d z) = 0. Using the result (d f)/(d z) = (df)/(dx) (dx)/(dz) + (df)/(dy) (dy)/(dz) gives the anti-analytic version of the Cauchy-Riemann equations as (d u)/(d x) | = | -(d v)/(d y) (d v)/(d x) | = | (d u)/(d y).

analytic function | Cauchy-Riemann equations