NUMERICAL CALCULUS PACKAGE SYMBOL

NSeries

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

Details Details

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:
Radius 1 radius of circle on which f is sampled

WorkingPrecision MachinePrecision precision used in internal computations