Difference between revisions of "Manuals/calci/GAMMALN"
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*This function gives the natural logarithm of the absolute value of the Gamma Function. | *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. | *The functions Digamma and Trigamma are the first and second derivatives of the logarithm of the Gamma Function. | ||
| − | *This is often called the | + | *This is often called the Polygamma function. |
*Gamma, Lgamma, Digamma and Trigamma functions are internal generic primitive functions. | *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</math> to the power <math>GAMMALN(x)</math>, where <math>x</math> is an integer, is same as <math>(x-1)!</math>. | ||
Revision as of 04:48, 4 December 2013
GAMMALN(x)
- 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 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} to the power 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(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
- GAMMALN(6) = 4.787491744416229
- GAMMALN(42) = 114.03421178146174
- GAMMALN(1) = 0.00018319639111644828(calci)
- 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 }