Title:        Symbolic and Numeric Computation of the Barnes
                Function
  Authors:      Victor Adamchik
  Affiliation:  Dept. Computer Science, Carnegie Mellon Univ.
  Abstract:
The Barnes G function, defined by a functional equation as a generalization of
the Euler gamma function,  is used in many applications of pure and applied
mathematics, and theoretical physics.  The theory of the Barnes function has
been related to certain spectral functions in mathematical physics, to the
study of functional determinants of Laplacians of the n-sphere, to the Hecke
L-functions, and to the Selberg zeta function.  There is a wide class of
definite integrals and infinite sums appeared in statistical physics (the Potts
model) and lattice theory which can be computed by means of the G function.
This talk presents new integral representations, asymptotic series and some
special values of the Barnes function.  An explicit representation by means of
the Hurwitz zeta function and its relation to the determinants of Laplacians
are also discussed.  Finally, we propose an efficient numeric procedure for
evaluating the G function.