Fast Discrete Finite Hankel Transform for Equations in a Thin Annulus

An algorithm is proposed for a fast discrete finite Hankel transform of a function in a thin annulus. The transform arises in a natural way in the Neumann boundary-value problem for the Poisson equation in an annulus when spectral methods are applied for its numerical solution. The proposed algorithm uses the limiting properties of eigenvalues and eigenfunctions of the Laplace operator as the annulus thickness goes to zero.