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IntegrateGaussLegendre Method

Approximation of the definite integral of an analytic smooth function by Gauss-Legendre quadrature. When either or both limits are infinite, the integrand is assumed rapidly decayed to zero as x -> infinity.

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 intervalBegin,
	double intervalEnd,
	int order = 128
)

Parameters

f  FuncDouble, Double
The analytic smooth function to integrate.
intervalBegin  Double
Where the interval starts.
intervalEnd  Double
Where the interval stops.
order  Int32  (Optional)
Defines an Nth order Gauss-Legendre rule. The order also defines the number of abscissas and weights for the rule. Precomputed Gauss-Legendre abscissas/weights for orders 2-20, 32, 64, 96, 100, 128, 256, 512, 1024 are used, otherwise they're calculated on the fly.

Return Value

Double
Approximation of the finite integral in the given interval.
See Also