StableDistributionSymmetricPDFSeriesSmallX Method

Imaginary part of the Fourier transformed derivative of the Kohlrausch function for low frequencies.

Namespace: Altaxo.Calc.Probability
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3179.0 (4.8.3179.0)

Syntax

public static double PDFSeriesSmallX(
	double z,
	double alpha
)

Parameters

z Double: Circular frequency.
alpha Double: Beta parameter.

Return Value

Double
Imaginary part of the Fourier transformed derivative of the Kohlrausch function for high frequencies, or double.NaN if the series not converges.

Remarks

This is the imaginary part of the Fourier transform (in Mathematica notation): Im[Integrate[D[Exp[-t^beta],t]*Exp[-I w t],{t, 0, Infinity}]]. The sign of the return value here is positive!.

Reference

StableDistributionSymmetric Class

Altaxo.Calc.Probability Namespace