Asymptotic solutions in the transition regions for scattered field by a conducting circular cylinder

We derive the asymptotic solutions for the scattering from a conducting circular cylinder applicable in each of the transition regions divided by the shadow boundary (SB) into the shadow and the lit side. The asymptotic solutions include an extended Pekeris caret function. We verify the continuity on the SB of the asymptotic shadow region solution and the asymptotic lit region solution. The validity of the asymptotic solutions derived here is confirmed by comparing with the exact solution.