  We study massive one-loop integrals by analytically continuing the Feynman
integral to negative dimensions as advocated by Halliday and Ricotta and
developed by Suzuki and Schmidt. We consider n-point one-loop integrals with
arbitrary powers of propagators in general dimension D. For integrals with m
mass scales and q external momentum scales, we construct a template solution
valid for all n which allows us to obtain a representation of the graph in
terms of a finite sum of generalised hypergeometric functions with m+q-1
variables. All solutions for all possible kinematic regions are given
simultaneously, allowing the investigation of different ranges of variation of
mass and momentum scales.
  As a first step, we develop the general framework and apply it to massive
bubble and vertex integrals. Of course many of these integrals are well known
and we show that the known results are recovered. To give a concrete new
result, we present expressions for the general vertex integral with one
off-shell leg and two internal masses in terms of hypergeometric functions of
two variables that converge in the appropriate kinematic regions. The kinematic
singularity structure of this graph is sufficiently complex to give insight
into how the negative-dimension method operates and gives some hope that more
complicated graphs can also be evaluated.
