Syntax. GAMMALN(x)
Definition. This function returns the natural logarithm of the gamma function (Γ(x)).
Arguments
x (required). The value for which you want to calculate GAMMALN()
If x isn’t a numeric expression, the GAMMALN() function returns the #VALUE!
error. If x is less than or equal to 0, the function returns the #NUM!
error.
The number e raised to the GAMMALN(i) power, where i is an integer, returns the same result as (i – 1).
Background. The GAMMALN() function returns the natural logarithm of the gamma function.
You will find more information about gamma distributions in the description of GAMMA.DIST().
The logarithm of a number is the exponent by which a fixed number, the base, has to be raised to produce that number. The following logarithms exist:
Natural logarithm to base e (Euler’s number = 2.72)
Logarithm to base 10
Logarithm to base 2
The logarithm (to base b) of a number y is the number by which base b has to be raised to produce number y. Therefore, the logarithm is an exponent, and the logarithm function is the inverse function of the exponential function (see Figure 12-66).
GAMMALN() is calculated as follows:
where
Example. Assume that you want to calculate GAMMALN() given the value 4. Figure 12-67 shows the calculation of GAMMALN().
The GAMMALN() function returns the natural logarithm, 1.7918, for the gamma function based on the parameters shown in Figure 12-67.
Sample Files
Use the GAMMALN worksheet in the Probability.xls or Probability.xlsx sample file. The sample files are found in the Chapter12 folder. For more information about the sample files, see the section titled Using the Sample Files.
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