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.


  • To use NSeries, you first need to load the Numerical Calculus Package using Needs["NumericalCalculus`"].
  • 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.
  • The result of NSeries is a SeriesData object.
  • If the result of NSeries is a Laurent series, then 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 2^(TemplateBox[{{{log, _, 2},  , {(, n, )}}}, Ceiling]+2).
  • The following options can be given:
  • Radius1radius of circle on which f is sampled
    WorkingPrecisionMachinePrecisionprecision used in internal computations

ExamplesExamplesopen allclose all

Basic Examples  (1)Basic Examples  (1)

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This is a power series for the exponential function around :

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Chop is needed to eliminate spurious residuals:

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Using extended precision may also eliminate spurious imaginaries:

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