  By working in QED, we obtain the electron, positron, and photon Parton
Distribution Functions (PDFs) of the unpolarised electron at the
next-to-leading logarithmic accuracy. The PDFs account for all of the universal
effects of initial-state collinear origin, and are key ingredients in the
calculations of cross sections in the so-called structure-function approach. We
present both numerical and analytical results, and show that they agree
extremely well with each other. The analytical predictions are defined by means
of an additive formula that matches a large-$z$ solution that includes all
orders in the QED coupling constant $\alpha$, with a small- and
intermediate-$z$ solution that includes terms up to ${\cal O}(\alpha^3)$.
