Manuals/calci/GAMMALN

GAMMALN(x)

• $x$ is the number

Description

• 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.

• This function will give the result as error when

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

Examples

1. GAMMALN(6) = 4.787491744416229
2. GAMMALN(42) = 114.03421178146174
3. GAMMALN(1) = 0.00018319639111644828(calci)
4. GAMMALN(-10) = NAN, because $x<0$

See Also

• GAMMADIST
• FACT
• LN

References

Gamma Distribution*