gives a numerical approximation to the sum f using Euler's transformation.


uses a step di in the sum.

Details and Options

  • To use EulerSum, you first need to load the Numerical Calculus Package using Needs["NumericalCalculus`"].
  • EulerSum is particularly good for working with alternating series and series whose terms have the form , where is a polynomial in .
  • EulerSum can be used for sums with both finite and infinite limits.
  • The following options can be given:
  • EulerRatioAutomaticparameter used in generalized Euler transformations
    ExtraTerms7number of terms to use during extrapolation
    Terms5number of terms to use before extrapolation
    WorkingPrecisionMachinePrecisionthe precision used in internal computations
  • Valid settings for EulerRatio are Automatic, a single ratio, or a list of ratios or {ratio,degree+1} pairs. In the case of a list, the various ratios are used successively in iterated Euler transformations.
  • With the default setting Automatic, the value used for EulerRatio is based on the ratio of successive terms in the series.
  • Valid settings for ExtraTerms are integers greater than 1. The default setting is 7.
  • The setting for ExtraTerms gives the number of terms to be used in the extrapolation process after the number of terms specified by the option Terms have been explicitly summed.
  • Valid settings for Terms are positive integers.