A new Weber-type transform
In this paper we introduce a new Weber-type transform pair for the representation of a function f(r) defined over the domain a < r < oo and which satisfies the Robin mixed boundary condition f{a) + Xf'(a) = 0. The orthogonality relationships of the transform kernels are derived in both the spatial and the spectral domains as well as Parseval's theorem. We apply this new Weber-type transform pair to solve a mixed boundary value problem in a system of planar layers.