We present the results of a calculation of the rate for the annihilati
on of an e(+) e(-) pair into a jet containing an energetic photon and
a single further jet at order alpha alpha(s). By comparing these resul
ts with the existing data on the photon + 1 jet rate from the ALEPH Co
llaboration, we make a first determination of the process independent
quark-to-photon fragmentation function Dq-->y(Z,mu p) at order alpha a
lpha(s). We also compare our prediction for the inclusive photon energ
y spectrum with the recent OPAL measurement. (C) 1997 Elsevier Science
B.V.