This is documentation for Mathematica 6, which was
based on an earlier version of the Wolfram Language.

# NSeries

 NSeries[f, {x, x0, n}] gives a numerical approximation to the series expansion of f about the point x=x0 including the terms (x-x0)-n through (x-x0)n.
• The function f must be numeric when its argument x is numeric.
• NSeries will construct standard univariate Taylor or Laurent series.
• NSeries samples f at points on a circle in the complex plane centered at x0 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.
• NSeries will not return a correct result if the disk centered at x0 contains a branch cut of f.
• If the result of NSeries 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.
• NSeries 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 22+log2[n].
• The following options can be given:
 Radius 1 radius of circle on which f is sampled WorkingPrecision MachinePrecision precision used in internal computations
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)
 Options   (2)
 Applications   (1)