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We construct the path integral formula in terms of ``multi-periodic''coherent state as an extension of the Nielsen-Rohrlich formula for spin. Wemake an exact calculation of the formula and show that, when a parametercorresponding to the magnitude of spin becomes large, the leading order term ofthe expansion coincides with the exact result. We also give an explicitcorrespondence between the trace formula in the multi-periodic coherent stateand the one in the ``generalized'' coherent state.Comment: 28 pages, late

Multi-periodic coherent states and the WKB exactness