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Abstract: The standard Fock functions that are the point of departure for this study are used in diffraction theory to describe the surface current on perfectly conducting convex scatterers. They are fairly accurate near the shadow boundary and in the shadow. There is also a reformulation in terms of these functions that describes the field in the lit region. In this study, a uniform counterpart to these functions is obtained for cylindrical geometry by means of integral representations. The numerical aspects of the evaluation of these integrals are discussed. High accuracy is achieved, also for the lit region. Asymptotic approximations for the uniform functions are obtained in the high frequency limit. These expansions could provide the same accuracy as the integral representation inside the lit domain of the scatterer. [Copyright &y& Elsevier]