Documentation/Calc Functions/GAMMA
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Function name:
GAMMA
Category:
Statistical Analysis
Summary:
Calculates the value of the gamma function for a specified real number. The gamma function extends the concept of the factorial function to non-integer and negative numbers.
Syntax:
GAMMA(Number)
Returns:
Returns a real number, which is the value of the gamma function for the number passed as argument.
Arguments:
Number is a real number, or a reference to a cell containing that number, for which the gamma function is to be calculated.
- If Number is non-numeric, then GAMMA reports a #VALUE! error.
- If Number is equal to 0, or equal to any negative integer, then GAMMA reports an invalid argument error (Err:502).
Additional details:
- The formula for the gamma function (represented by the Greek letter [math]\displaystyle{ \Gamma }[/math]) is usually expressed as:
- [math]\displaystyle{ \Gamma(x)~=~\int_{0}^{\infty } \: t^{x-1} \: e^{-t}\:dt }[/math]
- This formula is valid for any positive real number (x).
- In addition, the gamma function satisfies the following recursive relationship:
- [math]\displaystyle{ \Gamma(x+1)~=~x \: \Gamma(x) }[/math]
- This recursion enables the value of the gamma function to be evaluated for negative, non-integer numbers.
- The following figure shows a plot of the gamma function for numbers x in the range [-4, 4].
- For more information about the gamma function, visit Wikipedia's Gamma function page.
Examples:
Formula | Description | Returns |
---|---|---|
=GAMMA(A1) where cell A1 contains the number 10. | Calculates the gamma function for an input value of 10. Note that for positive integers (natural numbers), the relation [math]\displaystyle{ \Gamma(n)=(n-1)! }[/math] applies. In this case, [math]\displaystyle{ (10-1)!=9!=362880 }[/math], demonstrating the relation. | 362880 |
=GAMMA(-0.2) | Calculates the gamma function for an input value of -0.2. | -5.82114856862652 |
=GAMMA(0.8) | Calculates the gamma function for an input value of 0.8. This could also be calculated from the previous example, using the relation [math]\displaystyle{ \Gamma(x+1)=x \Gamma(x) }[/math]. [math]\displaystyle{ -0.2 \times -5.82114856862652 = 1.1642297137253 }[/math]. | 1.1642297137253 |
=GAMMA(-1.5) | Calculates the gamma function for an input value of -1.5. | 2.36327180120735 |
Related LibreOffice functions:
ODF standard:
Related (or similar) Excel functions:
GAMMA since v.2013.