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KohlrauschRe2SmallBeta Method

Real part of the Fourier transformed derivative of the Kohlrausch function for low frequencies, and beta<=1/20..

Namespace: Altaxo.Calc
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3261.0 (4.8.3261.0)
Syntax
C#
Copy
public static double Re2SmallBeta(
	double beta,
	double z
)

Parameters

beta  Double
Beta parameter.
z  Double
Circular frequency, must be much lesser than one.

Return Value

Double
Real part of the Fourier transformed derivative of the Kohlrausch function for low frequencies, or double.NaN if the series not converges.
Remarks
This is the real part of the Fourier transform (in Mathematica notation): Re[Integrate[-D[Exp[-t^beta],t]*Exp[-I w t],{t, 0, Infinity}]]. For beta smaller than one, the return value is always positive.
See Also