Truncation error estimates for generalized Hermite sampling

The generalized Hermite sampling uses samples from the function itself and its derivatives up to order r. In this paper, we investigate truncation error estimates for the generalized Hermite sampling series on a complex domain for functions from Bernstein space. We will extend some known techniques to derive those estimates and the bounds of Jagerman (SIAM J. Appl. Math. 14, 714–723 1966), Li (J. Approx. Theory 93, 100–113 1998), Annaby-Asharabi (J. Korean Math. Soc. 47, 1299–1316 2010), and Ye and Song (Appl. Math. J. Chinese Univ. 27, 412–418 2012) will be special cases for our results. Some examples with tables and figures are given at the end of the paper.