This funciton 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 γ(a, x) is defined only for a greater than zero. Although γ(a, x) is well defined for
x >-∞, this algorithm does not calculate γ(a, x) for negative x. For large a and sufficiently large x, γ(a, x) may overflow. γ(a, x) is bounded by G(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 4- 3  Contour Plot of g(a, x)

Example

In this example, γ(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

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