This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# NSeries

 gives a numerical approximation to the series expansion of f about the point including the terms through .
• The function f must be numeric when its argument x is numeric.
• will construct standard univariate Taylor or Laurent series.
• samples f at points on a circle in the complex plane centered at and uses InverseFourier. The option Radius specifies the radius of the circle.
• The region of convergence will be the annulus (containing the sampled points) where f is analytic.
• will not return a correct result if the disk centered at contains a branch cut of f.
• If the result of is a Laurent series, than the SeriesData object is not a correct representation of the series, as higher-order poles are neglected.
• No effort is made to justify the precision in each of the coefficients of the series.
• is unable to recognize small numbers that should in fact be zero. Chop is often needed to eliminate these spurious residuals.
• The number of sample points chosen is .
• The following options can be given:
 Radius 1 radius of circle on which f is sampled WorkingPrecision MachinePrecision precision used in internal computations
This is a power series for the exponential function around x=0:
Chop is needed to eliminate spurious residuals:
Using extended precision may also eliminate spurious imaginaries:
Needs["NumericalCalculus`"]
This is a power series for the exponential function around x=0:
 Out[2]=
Chop is needed to eliminate spurious residuals:
 Out[3]=
Using extended precision may also eliminate spurious imaginaries:
 Out[4]=
 Scope   (2)
Find expansions in the complex plane:
Find Laurent expansions about essential singularities:
Series will not find Laurent expansions about essential singularities:
 Options   (2)
Use Radius to pick the annulus within which the Laurent series will converge:
Laurent series for :