New analytical expressions for the diffraction integral in the case of a perfectly conducting wedge of an arbitrary angle illuminated by a plane wave or by a line source field are presented. They are indpendent of the poles in the original integrals and avoid the process of selection of the integer parameter in previous formulations, thus giving a continuous total field at the geometrical optics boundaries. The uniform solution formula in the case of a line source field illumination is obtained without using the asymptotic expansion of the Hankel functions in the cylindrical waves, which extends its validity in the near zone, when the electrical distance from the edge is less than unity. The proposed formulas allow a clearer physical interpretation of the diffraction phenomena and a more convenient and efficient calculation of the diffracted fields even in the region about the geometrical optics boundaries.