IMSL_GAMMAI

Syntax | Return Value | Arguments | Keywords | Discussion | Example | Errors | Version History

The IMSL_GAMMAI function evaluates the incomplete gamma function γ(a, x).

Note
This routine requires an IDL Advanced Math and Stats license. For more information, contact your ITT Visual Information Solutions sales or technical support representative.

Syntax

Result = IMSL_GAMMAI(a, x [, /DOUBLE])

Return Value

The value of the incomplete gamma function γ(a, x).

Arguments

a

Integrand exponent parameter. It must be positive.

x

Upper limit of integration. It must be nonnegative.

Keywords

DOUBLE

If present and nonzero, double precision is used.

Discussion

The incomplete gamma function, γ(a, x), is defined as follows:

The incomplete gamma function is defined only for a > 0. Although γ(a, x) is well-defined for x > –infinity, this algorithm does not calculate γ(a, x) for negative x. For large a and sufficiently large x, γ(a, x) may overflow. Gamma function γ(a, x) is bounded by Γ(a), and users may find this bound a useful guide in determining legal values for a.

Example

Plot the incomplete gamma function over [0.1, 1.1] x [0, 4]. The results are shown in Figure 12-6.

x = 4. * FINDGEN(25)/24 
a = 1e-1 + FINDGEN(25)/24 
b = FLTARR(25, 25) 
FOR i = 0, 24 DO b(i, *) = IMSL_GAMMAI(a(i), x) 
!P.Charsize = 2.5 
SURFACE, b, a, x, XTitle = 'a', YTitle = 'X' 

Figure 12-6: Incomplete Gamma Function Plot

Errors

Fatal Errors

MATH_NO_CONV_200_TS_TERMS—Function did not converge in 200 terms of Taylor series.

MATH_NO_CONV_200_CF_TERMS—Function did not converge in 200 terms of the continued fraction.

Version History