Truncation error for the generalized Bessel type sampling series

Numerous upper bounds for the truncation error of the Shannon sampling expansion associated with the Fourier transforms are available in the literature. In this paper we derive an upper bound for the truncation error of the generalized sampling expansion associated with the Hankel (Bessel) transform. A clear example of the application of such series is in the analysis of optical systems with circular symmetry. A lower bound for the Bessel function J_m(j_?,N+iy), which agrees with the known asymptotic one and is necessary to this analysis, is derived. The method, which employs complex contour integration, can be applied to other generalized sampling expansions.