Derivative Uniform Sampling via Weierstrass σ(z). Truncation Error Analysis in

Abstract

Abstract In the entire functions space consisting of at most second order functions such that their type is less than πq/(2s 2) it is valid the q-order derivative sampling series reconstruction procedure, reading at the von Neumann lattice {s(m + ni)| (m, n) ∈ } via the Weierstrass σ(·) as the sampling function, s > 0. The uniform convergence of the sampling sums to the initial function is proved by the circular truncation error upper bound, especially derived for this reconstruction procedure. Finally, the explicit second and third order sampling formulæ are given.