NUMERICAL CALCULUS 程序包 符号

# NSeries

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

## 更多信息更多信息

• 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 .
• The following options can be given:
•  Radius 1 radius of circle on which f is sampled WorkingPrecision MachinePrecision precision used in internal computations

## 范例范例打开所有单元关闭所有单元

### 基本范例 (1)基本范例 (1)

This is a power series for the exponential function around :

 Out[2]=

Chop is needed to eliminate spurious residuals:

 Out[3]=

Using extended precision may also eliminate spurious imaginaries:

 Out[4]=

## 教程教程

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