  We present a detailed study of photon production in hadronic events in
electron-positron annihilation at LEP energies. We show that estimates of the
inclusive photon spectrum using the quark-to-photon fragmentation function
determined using the ALEPH `photon' +~1 jet data agree well with the
observations of the OPAL collaboration. This agreement shows that the photon
fragmentation function determined in this way can be used for inclusive
observables. We also compare next-to-leading order and beyond leading logarithm
predictions obtained using the numerically resummed solutions of the
fragmentation function evolution equation of Bourhis, Fontannaz and Guillet and
Gl\"uck, Reya and Vogt with the data. Moreover, in order to check the general
behaviour of the fragmentation function, we consider an analytic series
expansion in the strong coupling. We find that the parameterizations are
inaccurate at large $x$ values. While the OPAL data is in broad agreement with
estimates based on any of these approaches, the ALEPH data prefers the resummed
BFG parameterization. Finally, there is some ambiguity as to whether the
fragmentation function is treated as ${\cal O}(\alpha)$ or ${\cal
O}(\alpha/\alpha_s)$. We show that at present this ambiguity affects mainly the
prediction for the `photon' +~1 jet rate at large $z$.
