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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:

FACT

GAMMALN

GAMMALN.PRECISE

ODF standard:

Section 6.18.31, part 2

Related (or similar) Excel functions:

GAMMA since v.2013.