GAMMAI Function

Evaluates the incomplete gamma function g(x, y).

Usage

result = GAMMAI(x, y)

Input Parameters

x—Parameter of the incomplete gamma function is to be evaluated. x must be positive.

y—Point at which the incomplete gamma function is to be evaluated. y must be nonnegative.

Returned Value

result—The value of the incomplete gamma function g(x, y).

Input Keywords

Double—If present and nonzero, double precision is used.

Discussion

The incomplete gamma function, g(x, y), is defined to be:

 

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

Example

Evaluates the incomplete gamma function at x = 1 and y = 3.

x  =  1.0

y  =  3.0

ans  =  GAMMAI(x, y)

PRINT, 'incomplete gamma(', x, ',', y, ') =', ans

; PV-WAVE prints: incomplete gamma( 1.00000, 3.00000) = 0.950213

Fatal Errors

STAT_NO_CONV_200_TS_TERMS—The function did not converge in 200 terms of Taylor series.

STAT_NO_CONV_200_CF_TERMS—The function did not converge in 200 terms of the continued fraction.