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ErrorFunctionFaddeeva(Complex) Method

Given a complex number z = (x,y), this subroutine computes the value of the Faddeeva function w(z) = exp(-z^2)*erfc(-i*z), where erfc is the complex complementary error function and i means sqrt(-1).

Namespace: Altaxo.Calc
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3179.0 (4.8.3179.0)
Syntax
C#
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public static Complex Faddeeva(
	Complex z
)

Parameters

z  Complex
The function argument.

Return Value

Complex
The faddeeva function w(z).
Remarks
C#
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The accuracy of the algorithm for z in the 1st and 2nd quadrant
is 14 significant digits; in the 3rd and 4th it is 13 significant
digits outside a circular region with radius 0.126 around a zero
of the function.

All real variables in the program are double precision.
The parameter M_2_SQRTPI equals 2/sqrt(pi).

The routine is not underflow-protected but any variable can be
put to 0 upon underflow;

The routine is overflow-protected: Matpack::Error() is called.

References:

(1) G.P.M. Poppe, C.M.J. Wijers; More Efficient Computation of
    the Complex64T Error-Function, ACM Trans. Math. Software,
    Vol. 16, no. 1, pp. 47.
(2) Algorithm 680, collected algorithms from ACM.

The Fortran source code was translated to C++ by B.M. Gammel
and added to the Matpack library, 1992.

Last change: B. M. Gammel, 18.03.1996 error handling
See Also