  It is standard in theoretical neutrino astrophysics to use a broken power law
approximation, based on the Band function, to describe the average photon flux
of the prompt emission of Gamma-Ray Bursts. We will show that this
approximation overestimates the contribution of high energy gamma-rays (and
underestimates low energy gamma-rays). As a consequence models that rely on
this approximation overestimate neutrino event rate by a factor of approx 2
depending on Earth's column density in the direction of the GRB. Furthermore
the characteristic energy of neutrinos that trigger a km^3 detector is
typically 10^{16} eV, higher than previously predicted. We also provide a new
broken power law approximation to the Band function and show that it properly
represents the photon spectra.
