(definition)

**Definition:**
The gamma function of n, written Γ(n), is ∫ _{0}^{∞} e^{-x}x^{n-1}dx. Recursively Γ(n+1) = nΓ(n). For non-negative integers Γ(n+1) = *n!*.

**See also**
*Stirling's formula*.

*Note:
The gamma function is defined for all numbers whereas factorial is (strictly) only defined for non-negative integers.*

Author: PEB

MathWorld's gamma function

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Entry modified 17 December 2004.

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Cite this as:

Paul E. Black, "gamma function", in
*Dictionary of Algorithms and Data Structures* [online], Vreda Pieterse and Paul E. Black, eds. 17 December 2004. (accessed TODAY)
Available from: https://www.nist.gov/dads/HTML/gammaFunction.html