A new algorithm for summing divergent series Part 2: A two-component Borel summability model

摘要

If S(1n) ∼ Σ eS/ns is a descending series in n, and |eS| ultimately increases approximately as (2s)!, then the new two-component Borel algorithm, with quadratic terms in the integrands involved, is suggested as a summing technique. The linear equations which arise have been triangulated, so that approximants to the original series are simple to set up and not as subject to round-off error as other approaches.