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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle e</math to the power <math>{GAMMALN(x)}} , where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x} is an integer, is same as Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (x-1)!} .

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle GAMMALN=LN(GAMMA(x))} ,

where

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\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.

• This function will give the result as error when

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x}
 is non-numeric and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x \le 0}
.

Examples

1. GAMMALN(6) = 4.787491744416229
2. GAMMALN(42) = 114.03421178146174
3. GAMMALN(1) = 0.00018319639111644828(calci)
4. GAMMALN(-10) = NAN, because Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x<0 }

See Also

• GAMMADIST
• FACT
• LN

References

Gamma Distribution*