Let J(mu) denote the Bessel function of order mu. For alpha > -1, the
system x(-alpha/2-1/2)J(alpha+2n+1)(x1/2), n = 0, 1, 2,..., is orthogo
nal on L2((0, infinity), x(alpha) dx). In this paper we study the mean
convergence of Fourier series with respect to this system for functio
ns whose Hankel transform is supported on [0, 1].