The IMSL_GAMMA_ADV function evaluates the real gamma function.

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

The gamma function, Γ(x), is defined to be:

For x < 0, the above definition is extended by analytic continuation.

The gamma function is not defined for integers less than or equal to zero. It underflows for x << 0 and overflows for large x. It also overflows for values near negative integers.


In this example, Γ(1.5) is computed and printed.

x	=	1.5
PRINT, 'Gamma(', x, ') =', ans

IDL prints:

Gamma( 1.50000) = 0.886227


Alert Errors

STAT_SMALL_ARG_UNDERFLOW: The parameter x must be large enough that Γ(x) does not underflow. The underflow limit occurs first for parameters close to large negative half integers. Even though other parameters away from these half integers may yield machine-representable values of Γ(x), such parameters are considered illegal.

Warning Errors

STAT_NEARR_NEG_INT_WARN: The result is accurate to less than one-half precision because x is too close to a negative integer.

Fatal Errors

STAT_ZERO_ARG_OVERFLOW: The parameter for the gamma function is too close to zero.

STAT_NEAR_NEG_INT_FATAL: The parameter for the function is too close to a negative integer.

STAT_LARGE_ARG_OVERFLOW: The function overflows because x is too large.

STAT_CANNOT_FIND_XMIN: The algorithm used to find xmin failed. This error should never occur.

STAT_CANNOT_FIND_XMAX: The algorithm used to find xmax failed. This error should never occur.



Return Value

The value of the gamma function Γ(x).



Point at which the gamma function is to be evaluated.


DOUBLE (optional)

If present and nonzero, double precision is used.

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