Let $E$ and $F$ be vector bundles on a smooth projective variety, say.
A. Lascoux ("Classes de Chern d'un produit tensoriel", C. R. Acad. Sci. Paris Sér. A-B 286 (1978), no. 8, A385–A387) gave formulas for the Chern classes of $E \otimes F$, $Sym^2 E$ and $\bigwedge^2 E$ in terms of the Chern classes of $E$ and $F$.
Unfortunately, I don't have access to Lascoux's article, and a bit of Googling didn't find them reproduced elsewhere.
Does anyone know another reference (preferably freely available online) where these formulas are written down?
Edit: In the comments, Robert Bryant suggests Hirzebruch's book "Topological methods in algebraic geometry" as a reference. Indeed, there is a formula there for the generating function for the Chern classes of $E \otimes F$and $\bigwedge^p E$, namely the obvious thing you get from the splitting principle and Whitney sum formula. So this gives you some answer in terms of Chern roots of $E$ and $F$.
But he content of Lascoux's formulas (I guess; I mean, I haven't actually seen them) is to rearrange this into an expression just in terms of the Chern classes of $E$ and $F$. I can probably (he claimed) do this in whatever case I care about, but the real intent of my question is actually to get a reference.
Best Answer
You say you don't have access to Lascoux's paper, but it is actually available online at the BNF: