Legacy Document

gamma

You can use the gamma function to perform $Gamma(x)$ .

double_t gamma (double_t x);

x

Any positive floating-point number.

DESCRIPTION

The gamma function performs $Gamma(x)$ .

$gamma(x)\; =\; Gamma(x)\; =$₀ e^-tt^x+-1dt

The gamma function reaches overflow very fast as x approaches + . For large values, use the lgamma function (described in the next section) instead.

EXCEPTIONS

When x is finite and nonzero, either the result of $gamma(x)$ is exact or it raises one of the following exceptions:

• inexact (if the result must be rounded or an overflow occurs)
• invalid (if x is a negative integer)
• overflow (if the result is outside the range of the data type)

SPECIAL CASES

Table 10-37 shows the results when the argument to the gamma function is a zero, a NaN, or an Infinity, plus other special cases for the gamma function.

Special cases for the gamma function

Operation	Result	Exceptions raised
$gamma(x)$ for negative integer x	NaN	Invalid
$gamma(+0)$	NaN	Invalid
$gamma(-0)$	NaN	Invalid
$gamma(NaN)$	NaN	None[61]
$gamma(+$ )	+	Overflow
$gamma(-$ )	NaN	Invalid

EXAMPLES

z = gamma(-1.0);  /* z = NAN. The invalid exception is raised. */
z = gamma(6);     /* z = 120 */

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[61] If the NaN is a signaling NaN, the invalid exception is raised.