Difference between revisions of "Manuals/calci/GAMMALN"

Revision as of 23:35, 5 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 $etothepower{GAMMALN(x)}$ , where $x$ is an integer, is same as $(x-1)!$ .

Failed to parse (unknown function "\GAMMA"): {\displaystyle GAMMALN=LN(\GAMMA(x))} ,

where

Failed to parse (unknown function "\GAMMA"): {\displaystyle \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  to the power {GAMMALN(x)}</math>, where <math>x</math> is an integer, is same as <math>(x-1)!</math>.
-:<math>GAMMALN=LN(GAMMA(x))</math>,
+:<math>GAMMALN=LN(\GAMMA(x))</math>,
 where
-: <math>GAMMA(x) = \int\limits_{0}^{\infty} t^{x-1} e^{-t} dt</math>
+: <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