A new algorithm for summing divergent series Part 1. Basic theory and illustrations

摘要

If S(1n) is a descending series in n for a Stieltjes continued fractions, polynomials A(n), B(n) are chosen so that A(n) + B(n) S(1n) has a set of coefficients of powers of n (and n−1) equal to those in a given divergent series T(1n). The polynomials A(n), B(n) are related to the continued fraction convergents. A number of choices of S are discussed and asymptotic formulae developed.