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KohlrauschReIm Method

Fourier transformed derivative of the Kohlrausch function for all frequencies. In dependence on the parameters, either a series expansion (accuracy ca. 1E-14) or a bivariate Akima spline (accuracy 1E-4) is used.

Namespace: Altaxo.Calc
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3179.0 (4.8.3179.0)
Syntax
C#
Copy
public static Complex ReIm(
	double beta,
	double w
)

Parameters

beta  Double
Beta parameter (0..1).
w  Double
Circular frequency.

Return Value

Complex
Fourier transformed derivative of the Kohlrausch function, or Complex.NaN if the function can not be evaluated (can happen for beta smaller than 1/64).
Remarks
This is the imaginary part of the Fourier transform (in Mathematica notation): Integrate[-D[Exp[-t^beta],t]*Exp[-I w t],{t, 0, Infinity}]. For beta smaller than one, this is a retardation function, so the real part is positive and the imaginary part is negative.

Wanted! Who can contribute to a more accurate interpolation between the points? (The points itself are calculated with an accuracy of 1E-18.)

See Also