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KohlrauschIm Method

Imaginary part of the 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 double Im(
	double beta,
	double w
)

Parameters

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

Return Value

Double
Real part of the Fourier transformed derivative of the Kohlrausch function, or double.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): Im[Integrate[-D[Exp[-t^beta],t]*Exp[-I w t],{t, 0, Infinity}]]. For beta smaller than one, the return value is always 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