Recently, Kim and Imamura and Yokoyama derived an exact formula for
superconformal indices in three-dimensional field theories. Using their
results, we prove analytically the equality of superconformal indices in some
U(1)-gauge group theories related by the mirror symmetry. The proofs are based
on the well known identities of the theory of q-special functions. We also
suggest the general index formula taking into account the U(1)J global
symmetry present for abelian theories.Comment: 17 pages; minor change
