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GammaRelatedGammaIT(Double, Double) 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#
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public static double GammaIT(
	double x,
	double a
)

Parameters

x  Double
The function argument x.
a  Double
The function argument a.

Return Value

Double
Tricomi's incomplete gamma function of x and a.
Remarks
C#
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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