Sums, products, limits and extrapolation

Summation (fsum, nsum, sumem)

Products (fprod, nprod)

Limits (limit)

Extrapolation (richardson, shanks)

The following functions provide a direct interface to extrapolation algorithms. nsum() and limit() essentially work by calling the following functions with an increasing number of terms until the extrapolated limit is accurate enough.

The following functions may be useful to call directly if the precise number of terms needed to achieve a desired accuracy is known in advance, or if one wishes to study the convergence properties of the algorithms.