Todd class ($\mathrm{td}(E)={\prod }_j\frac{x_j}{1-e^{-x_j}}$)

Here the $x_j$ are the formal Chern roots of a vector bundle. The degree-four term is $(c_1^2+c_2)/12$. Applied to the tangent bundle of a compact complex surface, Riemann–Roch for the structure sheaf gives the Noether formula.