  We present analysis from simultaneous FUSE, ASCA, and EUVE observations, as
well as a reanalysis of archival HST spectra, from the extreme Narrow-line
Seyfert 1 Galaxy RE 1034+39 (KUG 1031+398). RE 1034+39 has an unusually hard
spectral energy distribution (SED) that peaks in the soft X-rays. Its emission
lines are unusual in that they can all be modelled as a Lorentzian centered at
the rest wavelength with only a small range in velocity widths. In order to
investigate whether the unusual SED influences the emission line ratios and
equivalent widths, we present three complementary types of photoionization
analysis. The FUSE spectrum was particularly important because it includes the
high-ionization line OVI. First, we use the photoionization code Cloudy and the
SED developed from the coordinated observations to confirm that the emission
lines are consistent with observed hard SED. The best model parameters were an
ionization parameter log(U) ~ -2 and a hydrogen number density log(n_H)=9.75
[cm^-2]. Second, we present a Locally Optimally-emitting Cloud model. This
model produced enhanced OVI as observed, but also yielded far too strong MgII.
Third, we develop a series of semi-empirical SEDs, run Cloudy models, and
compare the results with the measured values using a figure of merit (FOM). The
FOM minimum indicates similar SED and gas properties as were inferred from the
one-zone model using the RE 1034+39 continuum. Furthermore, the FOM increases
sharply toward softer continua, indicating that a hard SED is required by the
data in the context of a one-zone model.
