  In this paper, new analytic formulas for one-loop contributing to Higgs decay
channel $H \rightarrow Z\gamma$ are presented in terms of hypergeometric
functions. The calculations are performed by following the technique for tensor
one-loop reduction developed in [A.~I.~Davydychev, Phys.\ Lett.\ B {\bf 263}
(1991) 107]. For the first time, one-loop form factors for the decay process
are shown which are valid at arbitrary space-time dimension $d$.
