Nested summation symbols and perturbation theory

Abstract

A new mathematical concept, the nested summation symbol (NSS) has been developed. This concept is attached to a mathematical linear operator directly related to the summation symbols. After a discussion on its properties, we investigate the potential usefulness of this symbol in the developing of sequential and parallel computational algorithms, constituting a powerful link between mathematical formalism and high level languages programming. A NSS is well suited in order to express some kind of mathematical formulae and to implement them in any computational environment. In this sense, NSSs are directly related toartificial intelligence techniques. Nested sums are connected withgeneralized nested do loop (GNDL) structures, a programming concept developed in our laboratory. This paper shows an application of the NSS. The NSS concept has been used to obtain in a compact form the expressions of the general energy and wavefunction corrections associated to the perturbation theory under the Brillouin-Wigner or the Rayleigh-Schrodinger formalisms.