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ContourIntegrateGaussLegendre Method

Approximation of the definite integral of an analytic smooth complex function by double-exponential 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 Complex GaussLegendre(
	Func<double, Complex> f,
	double intervalBegin,
	double intervalEnd,
	int order = 128
)

Parameters

f  FuncDouble, Complex
The analytic smooth complex function to integrate, defined on the real domain.
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

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