A recursive algorithm for Pade´-Hermite approximations
USSR Computational Mathematics and Mathematical Physics
Numerical study of bifurcations by analytic continuation of a function defined by a power series
SIAM Journal on Applied Mathematics
A case study of methods of series summation: Kelvin-Helmholtz instability of finite amplitude
Journal of Computational Physics
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
| Hi-index | 7.29 |
We introduce a new form of differential approximant for the summation of power series. The method is a special type of Padé-Hermite approximant. It consists of a high-order linear differential equation with polynomial coefficients that is satisfied approximately by the partial sum of the power series. This method is able to reproduce the polylogarithmic functions exactly. Numerical evidence suggests that this is currently one of the best methods of singularity analysis for many problems.