A method is given for determining the coefficients an in the ‘dual’ Fourier—Bessel series where −1 < p < 1, F(r) is specified and αn is a positive root of Jv(αna) = 0. Such series arise in the solution of potential problems in which the application of a finite Hankel transform is appropriate and in which one of the boundary conditions is a ‘mixed’ one. As an illustration, the method is applied to find the potential due to an electrified circular disk situated inside an earthed coaxial infinite hollow cylinder. This shows that useful results can be obtained provided that the radius of the cylinder is sufficiently large.