Difference between revisions of "Manuals/calci/GAMMALN"
Jump to navigation
Jump to search
(Created page with "<div id="6SpaceContent" class="zcontent" align="left"> <font size="3"><font face="Times New Roman">'''GAMMALN'''('''x''')</font></font> <font size="3"><font face="Times ...") |
|||
| Line 1: | Line 1: | ||
| − | <div | + | <div style="font-size:30px">'''GAMMALN(x)'''</div><br/> |
| + | *Where 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, The gamma, lgamma, digamma and trigamma functions are internal generic primitive functions. | ||
| + | *Normally the number e to the power GAMMALN(x), where x is an integer, is same as (x-1)!. *GAMMALN=LN(GAMMA(x))=,where GAMMA(x) = integral 0 to infinity t^{x-1} e^{-t} dt.and it is for all complex numbers except the negative integers and zero. | ||
| + | *This function will give the result as error when x is nonnumeric and x<=0. | ||
| + | ==Examples== | ||
| + | #GAMMALN(6)=4.787491744416229 | ||
| + | #GAMMALN(42)=114.03421178146174 | ||
| + | #GAMMALN(1)=0.00018319639111644828(calci)=-0.00000000004171(Excel) approximate to 0. | ||
| + | #GAMMALN(-10)=NAN,because x<0 | ||
| + | ==See Also== | ||
| + | *[[Manuals/calci/GAMMADIST | GAMMADIST ]] | ||
| + | *[[Manuals/FACT | FACT]] | ||
| + | *[[Manuals/calci/LN | LN]] | ||
| − | + | ==References== | |
| − | + | [http://en.wikipedia.org/wiki/Gamma_distribution| Gamma Distribution]* | |
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | | | ||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
Revision as of 04:55, 4 December 2013
GAMMALN(x)
- Where 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, The gamma, lgamma, digamma and trigamma functions are internal generic primitive functions.
- Normally the number e to the power GAMMALN(x), where x is an integer, is same as (x-1)!. *GAMMALN=LN(GAMMA(x))=,where GAMMA(x) = integral 0 to infinity t^{x-1} e^{-t} dt.and it is for all complex numbers except the negative integers and zero.
- This function will give the result as error when x is nonnumeric and x<=0.
Examples
- GAMMALN(6)=4.787491744416229
- GAMMALN(42)=114.03421178146174
- GAMMALN(1)=0.00018319639111644828(calci)=-0.00000000004171(Excel) approximate to 0.
- GAMMALN(-10)=NAN,because x<0