Multivariate form of Hermite sampling series

In this paper, we establish a new multivariate Hermite sampling series involving samples from the function itself and its mixed and non-mixed partial derivatives of arbitrary order. This multivariate form of Hermite sampling will be valid for some classes of multivariate entire functions, satisfying certain growth conditions. We will show that many known results included in Commun Korean Math Soc, 2002, 17: 731–740, Turk J Math, 2017, 41: 387–403 and Filomat, 2020, 34: 3339–3347 are special cases of our results. Moreover, we estimate the truncation error of this sampling based on localized sampling without decay assumption. Illustrative examples are also presented.