Complete solutions for the diaphanous wedge, meaning a wedge with iden
tical wavenumbers inside and outside the wedge, are presented. The res
ults are obtained from an integral equation for the fields on the wedg
e, which is solved by the Mellin and Kantorovich-Lebedev transforms in
the static and dynamic cases, respectively, Pertinent formulations of
Gegenbauer's addition theorems play an important part in the derivati
on of the results, which are presented in closed form.