  We construct the path integral formula in terms of ``multi-periodic''
coherent state as an extension of the Nielsen-Rohrlich formula for spin. We
make an exact calculation of the formula and show that, when a parameter
corresponding to the magnitude of spin becomes large, the leading order term of
the expansion coincides with the exact result. We also give an explicit
correspondence between the trace formula in the multi-periodic coherent state
and the one in the ``generalized'' coherent state.
