Asymptotic and other formulas are derivedab initiofor the field diffracted by a perfectly conducting wedge when illuminated by a line source. In the transition zone between lit and shadowed regions, the field is decomposed into image and diffraction terms which enable the formulas to be used throughout the region for self-consistent field analyses. The wedge-diffraction functions are finding a growing application in the investigation of electromagnetic problems in which the dimensions are too large for waveguide-mode analysis, but too small for geometric optics to apply. Various formulas are scattered throughout the literature. In this paper, they are derived from first principles and presented in a form in which the areas of use are indicated, and the important transition zone near a shadow boundary is explained in some detail.