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.

X — The upper limit of the integral definition of GAMI. (Input)
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 1,  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