Difference between revisions of "Manuals/calci/GAMMALN"

Revision as of 04:41, 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 $e$ to the power $GAMMALN(x)$ , 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 7: / Line 7: @@
 *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>.
-*<math>GAMMALN=LN(GAMMA(x))</math>, where:
+:<math>GAMMALN=LN(GAMMA(x))</math>,
- <math>GAMMA(x) = \int\limits_{0}^{\infty} t^{x-1} e^{-t} dt</math>
+ where
-and it is for all complex numbers except the negative integers and zero.
+: <math>GAMMA(x) = \int\limits_{0}^{\infty} t^{x-1} e^{-t} dt</math>
+it is for all complex numbers except the negative integers and zero.
 *This function will give the result as error when
   <math>x</math> is non-numeric and <math>x \le 0</math>.
 ==Examples==
 #GAMMALN(6) = 4.787491744416229