# Gamma Functions and Related Functions

## FACTORIAL FUNCTION

ROUTINE DESCRIPTION
FAC Evaluates the factorial of the argument.
BINOM Evaluates the binomial coefficient.

## GAMMA FUNCTIONS

ROUTINE DESCRIPTION
GAMMA Evaluates the complete gamma function.
GAMR Evaluates the reciprocal gamma function.
ALNGAM Evaluates the logarithm of the absolute value of the gamma function.
ALGAMS Returns the logarithm of the absolute value of the gamma function and the sign of gamma.

## INCOMPLETE GAMMA FUNCTIONS

ROUTINE DESCRIPTION
GAMI Evaluates the incomplete gamma function.
GAMIC Evaluates the complementary incomplete gamma function.
GAMIT Evaluates the Tricomi form of the incomplete gamma function.

## PSI FUNCTION

ROUTINE DESCRIPTION
PSI Evaluates the logarithmic derivative of the gamma function.
PSI1 Evaluates the second derivative of the log gamma function.

## POCHHAMMER'S FUNCTIONS

ROUTINE DESCRIPTION
POCH Evaluates a generalization of Pochhammer's symbol.
POCH1 Evaluates a generalization of Pochhammer's symbol starting from the first order.

## BETA FUNCTION

ROUTINE DESCRIPTION
BETA Evaluates the complete beta function.
ALBETA Evaluates the natural logarithm of the complete beta function for positive arguments.
BETAI Evaluates the incomplete beta function ratio.