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With the aid of the contour integration form of Hermite polynomial, a closed form expression for multidimensional Franck-Condon integrals between displaced distorted-rotated harmonic potential surfaces has been developed.Analytic expression formulas of two-, three-, and four-dimensional Franck-Condon factors were derived straightforwardly by using the properties of Hermite polynomials.In addition, this new method was applied to study the photoelectron spectra of H2CO.It was found that the simulated photoelectron spectra are good in consistent with the observed spectra.