Difference between revisions of "Manuals/calci/GAMMALN"
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<div style="font-size:30px">'''GAMMALN(x)'''</div><br/> | <div style="font-size:30px">'''GAMMALN(x)'''</div><br/> | ||
| − | *<math>x</math> is the number | + | *<math>x</math> is the number. |
| + | **GAMMALN(), returns the natural logarithm of the Gamma Function. | ||
| + | |||
==Description== | ==Description== | ||
*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 | + | *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( | + | :<math>GAMMALN=LN( \Gamma(x)</math>, |
where | where | ||
| − | : <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. | it is for all complex numbers except the negative integers and zero. | ||
*This function will give the result as error when | *This function will give the result as error when | ||
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#GAMMALN(42) = 114.03421178146174 | #GAMMALN(42) = 114.03421178146174 | ||
#GAMMALN(1) = 0.00018319639111644828(calci) | #GAMMALN(1) = 0.00018319639111644828(calci) | ||
| − | #GAMMALN(-10) = | + | #GAMMALN(-10) = #N/A (X <= 0) |
| + | |||
| + | ==Related Videos== | ||
| + | |||
| + | {{#ev:youtube|SAMTXAAKeug|280|center|GAMMA Distribution}} | ||
| + | |||
==See Also== | ==See Also== | ||
*[[Manuals/calci/GAMMADIST | GAMMADIST ]] | *[[Manuals/calci/GAMMADIST | GAMMADIST ]] | ||
| − | *[[Manuals/FACT | FACT]] | + | *[[Manuals/calci/FACT | FACT]] |
*[[Manuals/calci/LN | LN]] | *[[Manuals/calci/LN | LN]] | ||
==References== | ==References== | ||
| − | [http://en.wikipedia.org/wiki/Gamma_distribution | + | [http://en.wikipedia.org/wiki/Gamma_distribution Gamma Distribution]* |
| + | |||
| + | |||
| + | |||
| + | *[[Z_API_Functions | List of Main Z Functions]] | ||
| + | |||
| + | *[[ Z3 | Z3 home ]] | ||
Latest revision as of 04:58, 12 August 2020
GAMMALN(x)
- is the number.
- GAMMALN(), returns the natural logarithm of the Gamma Function.
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 , where is an integer, is same as .
, where 
.- ,
,where
it is for all complex numbers except the negative integers and zero.
- This function will give the result as error when
is non-numeric and .
.
Examples
- GAMMALN(6) = 4.787491744416229
- GAMMALN(42) = 114.03421178146174
- GAMMALN(1) = 0.00018319639111644828(calci)
- GAMMALN(-10) = #N/A (X <= 0)
Related Videos
See Also
References