A family of sampling theorems for the reconstruction of bandlimited functions from their samples is presented. Taking one or more additional samples is shown to yield more rapidly convergent series with lower truncation errors, as well as to facilitate the reconstruction of functions of polynomial growth on the real line. The theorems apply to both uniform sampling and a large class of non-uniform sampling sets. The additional samples may be values of the function itself and/or its derivatives. The general theory is illustrated by several examples and numerical experiments.
This is joint work with Hussain Al-Hammali (Yeoju Technical Institute in Tashkent) .