Computation of diverging sums based on a finite number of terms

Exactly Predictable Functions for Simple Neural Networks

“…Since the early works of Borel [32], Hardy [33] and many others, it was demonstrated that the divergence of certain series does not automatically mean that it becomes useless. In fact, there have been several analytical and computational techniques developed that permit us to associate a finite value with a diverging series [34,35]. To provide a simple example, the sequence S ≡ ∑ ∞ n=0 (−2) n can be associated with the finite value S = 1∕3 .…”

Space-time-resolved Breit-Wheeler process for a model system

“…We should point out that despite the approximations concerning the spatial dimensions, the fermions' spin directions, and non-vanishing mass of the model photons, due to its fundamental character this Hamiltonian (and its reduced versions) has been studied in a wide variety of contexts. For example, to name a few, this includes the examination of the origin of attractive and repulsive interfermionic forces due to the exchange of intermediating photons [23], the evolution of bare electrons into physical electrons under photon emission [24,25], a space-time resolved Compton scattering [26], the formation of fermion bound states in the perturbative and also Borel summable non-perturbative regimes [22,27,28].…”