This function evaluates the Tricomi form of the incomplete gamma function.
Function Return Value
GAMIT — Function value. (Output)
Required Arguments
A — The integrand exponent parameter as per the comments. (Input)
X — The upper
limit of the integral definition of GAMIT.
(Input)
It must be nonnegative.
FORTRAN 90 Interface
Generic: GAMIT (A, X)
Specific: The specific interface names are S_GAMIT and D_GAMIT.
FORTRAN 77 Interface
Single: GAMIT (A, X)
Double: The double precision function name is DGAMIT.
Description
The Tricomi's incomplete gamma function is defined to be
where γ(a, x) is the incomplete gamma function. See GAMI for the definition of γ(a, x).
The only general restriction on a is that it must not be too close to a negative integer such that the accuracy of the result is less than half precision. Furthermore, ǀγ*(a, x)ǀ must not underflow or overflow. Although γ*(a, x) is well defined for x >-∞, this algorithm does not calculate γ*(a, x) for negative x.
A slight deterioration of two or three digits of accuracy will occur when GAMIT is very large or very small in absolute value because logarithmic variables are used. Also, if the parameter a is very close to a negative integer (but not quite a negative integer), there is a loss of accuracy which is reported if the result is less than half machine precision.
The function GAMIT is based on a code by Gautschi (1979).
Comments
Informational error
Type Code
3 2 Result of GAMIT(A, X) is accurate to less than one-half precision because A is too close to a negative integer.
Example
In this example, γ*(3.2, 2.1) is computed and printed.
USE GAMIT_INT
USE UMACH_INT
IMPLICIT NONE
! Declare variables
INTEGER NOUT
REAL A, VALUE, X
! Compute
A = 3.2
X = 2.1
VALUE = GAMIT(A, X)
! Print the results
CALL UMACH (2, NOUT)
WRITE (NOUT,99999) A, X, VALUE
99999 FORMAT (' GAMIT(', F6.3, ',', F6.3, ') = ', F6.4)
END
Output
GAMIT( 3.200, 2.100) = 0.0284
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