NESTED SUMMATION SYMBOLS AND PERTURBATION-THEORY

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, co nstituting a powerful link between mathematical formalism and high lev el languages programming. A NSS is well suited in order to express som e kind of mathematical formulae and to implement them in any computati onal environment. In this sense, NSSs are directly related to artifici al intelligence techniques. Nested sums are connected with generalized nested do loop (GNDL) structures, a programming concept developed in our laboratory. This paper shows an application of the NSS. The NSS co ncept has been used to obtain in a compact form the expressions of the general energy and wavefunction corrections associated to the perturb ation theory under the Brillouin-Wigner or the Rayleigh-Schrodinger fo rmalisms.