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 .
- The following options can be given:
Radius 1 radius of circle on which f is sampled WorkingPrecision MachinePrecision precision used in internal computations
Examplesopen allclose all
Basic Examples (1)
Chop is needed to eliminate spurious residuals:
Series will not find Laurent expansions about essential singularities: