Conformal Powers of the Laplacian via Stereographic Projection

A new derivation is given of Branson's factorization formula for the conformally invariant operator on the sphere whose principal part is the $k$-th power of the scalar Laplacian. The derivation deduces Branson's formula from knowledge of the corresponding conformally invariant operator on Euclidean space (the $k$-th power of the Euclidean Laplacian) via conjugation by the stereographic projection mapping.