gives a numerical approximation to the sum using Euler's transformation.
uses a step di in the sum.
- 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:
EulerRatio Automatic parameter used in generalized Euler transformations ExtraTerms 7 number of terms to use during extrapolation Terms 5 number of terms to use before extrapolation WorkingPrecision MachinePrecision the precision used in internal computations
- Valid settings for EulerRatio are Automatic, a single ratio, or a list of ratios or 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.