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NUMERICAL CALCULUS PACKAGE SYMBOL
EulerSum
gives a numerical approximation to the sum 
using Euler's transformation.
uses a step di in the sum.
Details
- To use
, you first need to load the Numerical Calculus Package using Needs["NumericalCalculus`"]. 
is particularly good for working with alternating series and series whose terms have the form 
, where 
is a polynomial in 
.
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.
