Difference between revisions of "Manuals/calci/GAMMALN"

Revision as of 05:50, 4 December 2013

GAMMALN(x)

This function gives the natural logarithm of the absolute value of the Gamma Function.
The functions Digamma and Trigamma are the first and second derivatives of the logarithm of the Gamma Function.
This is often called the Polygamma function.
Gamma, Lgamma, Digamma and Trigamma functions are internal generic primitive functions.
Normally the number $e^{GAMMALN(x)}$ , where $x$ is an integer, is same as $(x-1)!$ .

GAMMALN=LN(GAMMA(x))

,

where

GAMMA(x)=\int \limits _{0}^{\infty }t^{x-1}e^{-t}dt

it is for all complex numbers except the negative integers and zero.

 $x$  is non-numeric and  $x\leq 0$ .

@@ Line 6: / Line 6: @@
 *This is often called the Polygamma function.
 *Gamma, Lgamma, Digamma and Trigamma functions are internal generic primitive functions.
-*Normally the number <math>e</math> to the power <math>GAMMALN(x)</math>, where <math>x</math> is an integer, is same as <math>(x-1)!</math>.
+*Normally the number <math>e^{GAMMALN(x)}</math>, where <math>x</math> is an integer, is same as <math>(x-1)!</math>.
 :<math>GAMMALN=LN(GAMMA(x))</math>,
 where