  The Fourier-Bessel expansion of a function on a circular disc yields a simple
series representation for the end-to-end probability distribution function
w(R,phi) encountered in a planar persistent random walk, where the direction
taken in a step depends on the relative orientation towards the preceding step.
For all but the shortest walks, the proposed method provides a rapidly
converging, numerically stable algorithm that is particularly useful for the
precise study of intermediate-size chains that have not yet approached the
diffusion limit. As a practical application, we examine the force-extension
diagram of various planar polymer chains. With increasing joint stiffness, a
marked transition from rubber-like behaviour to a form of elastic response
resembling that of a flexible rod is observed.
