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GammaRelatedGammaIT(Double, Double, Boolean) Method

GammaIT(x,a) evaluates Tricomi's incomplete gamma function defined by GammaIT = x**(-a)/Gamma(a) * integral from 0 to x of exp(-t) * t**(a-1.0) for a > 0.0 and by analytic continuation for a <= 0.0. Gamma(x) is the complete gamma function of x.

Namespace: Altaxo.Calc
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3179.0 (4.8.3179.0)
Syntax
C#
public static double GammaIT(
	double x,
	double a,
	bool bDebug
)

Parameters

x  Double
The function argument x.
a  Double
The function argument a.
bDebug  Boolean
If true, an exception is thrown if serious errors occur. If false, NaN is returned on errors.

Return Value

Double
Tricomi's incomplete gamma function of x and a.
Remarks
C#
GammaIT(x,a) is evaluated for arbitrary real values of a and for
non-negative values of x (even though GammaIT is defined for x < 0.0),
except that for x = 0 and a <= 0.0, GammaIT is infinite,
which is a fatal error.

The function and both arguments are double.
A slight deterioration of 2 or 3 digits accuracy will occur when
GammaIT 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 DGAMIT, 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:
  LnGamma(x)      - logarithm of the Gamma function
  LnGamma(x,sgn)  - logarithm and sign of the Gamma function
  RcpGamma(x)     - reciprocal of the Gamma function
  d9gmit(a,x,algap1,sgngam)
  d9lgit(a,x,algap1)
  d9lgic(a,x,alx)
See Also