Pseudoanalytic function

Summary

A pseudoanalytic function is a complex function that is "holomorphic relative to a pair of basis functions" $(F, G)$ instead of relative to the pair $(1, i)$. The notion was introduced by Lipman Bers to extend the theory of holomorphic functions to solutions of first-order elliptic systems in the plane. For smooth generating pairs, pseudoanalytic functions satisfy equations of the form $w_{\bar z} = a w + b \bar w$, and many theorems of complex analysis carry over to them.