  A new method for directly sampling the neutron resonance upscattering effect
is presented. Alternatives have relied on inefficient rejection sampling
techniques or large tabular storage of relative velocities. None of these
approaches, which require pointwise energy data, are particularly well suited
to the windowed multipole cross section representation. The new method called
multipole analytic resonance scattering (MARS) overcomes these limitations by
inverse transform sampling from the target relative velocity distribution where
the cross section is expressed in the multipole formalism. The closed form
relative speed distribution contains a novel special function we deem the
incomplete Faddeeva function: $$ w(z, x) = \frac{i}{\pi} \int_{-\infty}^x
\frac{e^{-t^2} dt}{z-t}. $$ We present the first results on its efficient
numerical evaluation.
