ABSTRACT
This chapter first deals with multi-dimensional analogs of the Bernoulli polynomials related to iterated Laplace operators (cf. W. Freeden [2011]). As in the one-dimensional theory, the multi-dimensional “Bernoulli polynomials” may be understood as Green’s functions for the Laplace operator Δ and the “boundary condition of Λ-lattice periodicity”, so that multivariate Euler summation formulas become accessible for regular regions.
