Polya Vector Field -

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

The Pólya field (\mathbfV_f) is exactly (w) — so it is a (gradient of a harmonic function, also curl-free and divergence-free locally). polya vector field

[ u_x = v_y, \quad u_y = -v_x. ]

The of (f) is defined as the vector field in the plane given by Let [ f(z) = u(x,y) + i,v(x,y) ]