lgamma

You can use the lgamma function to compute the natural logarithm of the absolute value of $Gamma(x)$ .

double_t lgamma (double_t x);

x

Any positive floating-point number.

DESCRIPTION

The lgamma function computes the natural logarithm of the absolute value of $Gamma(x)$ .

$lgamma(x)\; =\; log$_e(|Gamma(x)|) = ln(|Gamma(x)|)

EXCEPTIONS

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

• inexact (if the result must be rounded or an overflow occurs)
• overflow (if the result is outside the range of the data type)
• invalid (if x 0)

SPECIAL CASES

Table 10-38 shows the results when the argument to the lgamma function is a zero, a NaN, or an Infinity, plus other special cases for the lgamma function.

Special cases for the lgamma function

Operation	Result	Exceptions raised
$lgamma(x)$ for x < 0	NaN	Invalid
$lgamma(+0)$	NaN	Invalid
$lgamma(-0)$	NaN	Invalid
$lgamma(NaN)$	NaN	None[62]
$lgamma(+$ )	+	Overflow
$lgamma(-$ )	NaN	Invalid

EXAMPLES

z = lgamma(-1.0);    /* z = NAN. The invalid exception is 
                        raised. */
z = lgamma(3.41);    /* z = 1.10304. The inexact exception is 
                        raised. */

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