  We introduce a general expression which enables the parton distribution,
unintegrated over the parton transverse momentum, to be obtained from the
conventional parton densities. We use the formalism to study the effects of the
transverse momentum q_t of the incoming partonic system on the calculation of
the transverse momentum spectra of prompt photons produced in high energy pp
and p\bar{p} collisions. For the purposes of illustration, we use the double
logarithm approximation. For large q_t we calculate the effect directly from
the perturbative formalism, whereas for small q_t we bound the effect using two
extreme hypotheses. In both q_t domains we find that the shapes of the prompt
photon spectra are not significantly modified, although the cross sections are
enhanced.
