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Electromagnetic transverse electric wave scattering from a circumferential gap on a conducting circular waveguide is theoretically investigated. The Fourier transform/series technique is used to constitute a set of simultaneous equations for the discrete modal coefficients. Residue calculus is applied to obtain a fast-convergent series solution that is amenable to the numerical computations. Extensive calculations are performed to examine the effects of a gap on the radiation and scattering.