  We show that both perturbative and non-perturbative parts of universal
partition functions of Chern-Simons theory on 3d sphere are ratios of four over
four Barnes' quadruple gamma functions with arguments given by linear
combinations of universal parameters. Since nonperturbative part of partition
function is essentially a universal compact simple Lie group's volume, latter
appears to be expressed through quadruple Barnes' functions, also. For SU(N)
values of parameters recurrent relations on Barnes' functions give the proof of
level-rank duality of complete partition function, thus extending that duality
on non-integer level and rank. We note that integral representation of
universal partition function is defined on few disjoint regions in parameters'
space, corresponding to different signs of real parts of parameters, and
introduce a framework for discussion of analytic continuation of partition
functions(s) from these regions. Although initial integral representation is
symmetric under all permutations of parameters (which corresponds particularly
to $N \rightarrow -N$ duality of gauge theories with classical groups),
analytic continuations are not symmetric under transposition of parameters with
different signs of their real parts. For the particular case of SU(N)
Chern-Simons this asymmetry appears to be the Kinkelin's functional equation
(reflection relation) for Barnes' G-function.
