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Previous theoretical studies of distributed feedback fiber lasers (DFB-FLs) have largely relied on numerical simulations. In this paper, analytical expressions are derived for the resonant frequency and mode shape of a single-frequency DFB-FL structure, taking into account nonuniformities and phase errors. The analysis also accounts for spatial hole burning and "gain grating" effects under the assumption that the grating strength is large compared to the available gain. This applies, in particular, to low-gain erbium-doped DFB-FLs which are of substantial interest in sensor applications. An expression for the steady-state laser power is derived. It is also shown how the analysis can be extended to higher order modes, although this is not developed in detail.