Formal group law in topology

Definition

Let $R$ be a commutative ring. A (one-dimensional, commutative) formal group law over $R$ is a formal power series $F(x, y) \in R[\![x, y]\!]$ such that:

1. $F(x, y) \equiv x + y$ modulo terms of total degree at least $2$.
2. $F(x, F(y, z)) = F(F(x, y), z)$ in $R[\![x, y, z]\!]$.
3. $F(x, y) = F(y, x)$.

Let $E$ be a multiplicative generalized cohomology theory with coefficient ring $E^* = E^*(\mathrm{pt})$. A complex orientation of $E$ is a class $x \in \tilde E^2(\C P^\infty)$ whose restriction to $\tilde E^2(\C P^1) \cong E^0(\mathrm{pt})$ is the unit $1$. Then $E^*(\C P^\infty) = E^*[\![x]\!]$ and $E^*(\C P^\infty \times \C P^\infty) = E^*[\![x_1, x_2]\!]$, with $x_i$ pulled back from the $i$-th factor. Let $m \colon \C P^\infty \times \C P^\infty \to \C P^\infty$ classify the tensor product of the two universal line bundles. The formal group law of $(E, x)$ is the power series $F$ over $E^*$ with $m^*(x) = F(x_1, x_2)$. It satisfies the three conditions above, and it is homogeneous of degree $2$ when $x$, $x_1$ and $x_2$ have degree $2$.