NSeries


gives a numerical approximation to the series expansion of f about the point including the terms through .

DetailsDetails

  • To use , you first need to load the Numerical Calculus Package using Needs["NumericalCalculus`"].
  • 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.
  • The result of is a SeriesData object.
  • If the result of 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.
  • 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