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GammaRelatedGamma(Double, Double, Boolean) Method

Evaluate the complementary incomplete Gamma function Gamma(a,z0) = integral from z0 to infinity of exp(-t) * t**(a-1) The order of parameters is the same as the Mathematica function Gamma[a,z0]. Gamma(a,z0) is evaluated for arbitrary real values of A and for non-negative values of x (even though Gamma is defined for z0 < 0.0), except that for z0 = 0 and a <= 0.0, Gamma is undefined.

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 double Gamma(
	double a,
	double z0,
	bool bDebug
)

Parameters

a  Double
The function argument.
z0  Double
The lower boundary of integration.
bDebug  Boolean
If true, an exception is thrown if serious errors occur. If false, NaN is returned on errors.

Return Value

Double
Complementary incomplete Gamma function of arguments a and z0.
Remarks
C#
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A slight deterioration of 2 or 3 digits accuracy will occur when
GammaIC is very large or very small in absolute value, because log-
arithmic variables are used.  Also, if the parameter A is very close
to a negative integer (but not a negative integer), there is a loss
of accuracy, which is reported if the result is less than half
machine precision.

This is a translation from the Fortran version of DGAMIC, SLATEC, FNLIB,
CATEGORY C7E, REVISION 920528, originally written by Fullerton W.,(LANL)
to C++.

References:

(1) W. Gautschi, A computational procedure for incomplete
    gamma functions, ACM Transactions on Mathematical
    Software 5, 4 (December 1979), pp. 466-481.
(2) W. Gautschi, Incomplete gamma functions, Algorithm 542,
    ACM Transactions on Mathematical Software 5, 4
    (December 1979), pp. 482-489.

Routines called: d9gmit, d9gmic, d9lgic, d9lgit, LnGamma(x), LnGamma(x,a)
See Also