Polya Vector Field ●

Let [ f(z) = u(x,y) + i,v(x,y) ] be an analytic function on a domain (D \subset \mathbbC).

The of (f) is defined as the vector field in the plane given by polya vector field

[ \nabla u = (u_x, u_y) = (v_y, -v_x). ] Let [ f(z) = u(x,y) + i,v(x,y) ]

So (\mathbfV_f) is (solenoidal) — it has a stream function. Let [ f(z) = u(x