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DifferIntegrateGaussLegendre Method

Evaluates the Riemann-Liouville fractional derivative that uses the Gauss-Legendre integration.

Namespace: Altaxo.Calc
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3179.0 (4.8.3179.0)
Syntax
C#
Copy
public static double GaussLegendre(
	Func<double, double> f,
	double x,
	double order,
	double x0 = 0,
	int gaussLegendrePoints = 128
)

Parameters

f  FuncDouble, Double
The analytic smooth function to differintegrate.
x  Double
The evaluation point.
order  Double
The order of fractional derivative.
x0  Double  (Optional)
The reference point of integration.
gaussLegendrePoints  Int32  (Optional)
The number of Gauss-Legendre points.

Return Value

Double
Approximation of the differintegral of order n at x.
Remarks

order = 1.0 : normal derivative

order = 0.5 : semi-derivative

order = -0.5 : semi-integral

order = -1.0 : normal integral

See Also