Changes

<div style="font-size:30px">'''GAMMALN(x)'''</div><br/>

<div style="font-size:30px">'''GAMMALN(x)'''</div><br/>

*Where x is the number

*<math>x</math> is the number

==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 ‘polygamma’ function, The gamma, lgamma, digamma and trigamma functions are internal generic primitive functions.  

*This is often called the ‘Polygamma’ function.

*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.

*Gamma, Lgamma, Digamma and Trigamma functions are internal generic primitive functions.  

*This function will give the result as error when x is nonnumeric and x<=0.

*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>.

*<math>GAMMALN=LN(GAMMA(x))</math>, where:

<math>GAMMA(x) = \int\limits_{0}^{\infty} t^{x-1} e^{-t} dt</math>

and it is for all complex numbers except the negative integers and zero.

*This function will give the result as error when

<math>x</math> is non-numeric and <math>x \le 0</math>.

==Examples==

==Examples==

#GAMMALN(6)=4.787491744416229

#GAMMALN(6) = 4.787491744416229

#GAMMALN(42)=114.03421178146174

#GAMMALN(42) = 114.03421178146174

#GAMMALN(1)=0.00018319639111644828(calci)=-0.00000000004171(Excel) approximate to 0.

#GAMMALN(1) = 0.00018319639111644828(calci)

#GAMMALN(-10)=NAN,because x<0

#GAMMALN(-10) = NAN, because <math> x<0 </math>

==See Also==

==See Also==

*[[Manuals/calci/GAMMADIST | GAMMADIST ]]

*[[Manuals/calci/GAMMADIST | GAMMADIST ]]