GAMI
This function evaluates the incomplete gamma function.
Function Return Value
GAMI — Function value. (Output)
Required Arguments
A — The integrand exponent parameter. (Input)
It must be positive.
It must be positive.
X — The upper limit of the integral definition of GAMI. (Input)
It must be nonnegative.
It must be nonnegative.
FORTRAN 90 Interface
Generic: GAMI (A, X)
Specific: The specific interface names are S_GAMI and D_GAMI.
FORTRAN 77 Interface
Single: GAMI (A, X)
Double: The double precision function name is DGAMI.
Description
The incomplete gamma function is defined to be
The function (a, x) is defined only for a greater than zero. Although (a, x) is well defined for x >‑∞, this algorithm does not calculate (a, x) for negative x. For large a and sufficiently large x, (a, x) may overflow. (a, x) is bounded by Γ(a), and users may find this bound a useful guide in determining legal values of a.
Because logarithmic variables are used, a slight deterioration of two or three digits of accuracy will occur when GAMI is very large or very small.
Figure 6, Contour Plot of γ(a, x)
Example
In this example, (2.5, 0.9) is computed and printed.
USE GAMI_INT
USE UMACH_INT
IMPLICIT NONE
! Declare variables
INTEGER NOUT
REAL A, VALUE, X
! Compute
A = 2.5
X = 0.9
VALUE = GAMI(A, X)
! Print the results
CALL UMACH (2, NOUT)
WRITE (NOUT,99999) A, X, VALUE
99999 FORMAT (' GAMI(', F6.3, ',', F6.3, ') = ', F6.4)
END
Output
GAMI( 2.500, 0.900) = 0.1647
