Models for the Maclaurin tower of a simplicial functor via a derived Yoneda embedding

We prove that the Goodwillie tower of a weak equivalence preserving functor from spaces to spectra can be expressed in terms of the tower for stable mapping spaces. Our proof is motivated by interpreting the functors Pn and Dn as pseudo-differential operators which suggests certain ‘integral’ presentations based on a derived Yoneda embedding. These models allow one to extend computational tools available for the tower of stable mapping spaces. As an application we give a classical expression for the derivative over the basepoint.