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gamma.md

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title GAMMA
language en
description Returns the Gamma function value of x.

Description

Returns the Gamma function value of x. The Gamma function is defined as Γ(x) = ∫₀^∞ t^(x-1)e^(-t)dt for x > 0, and extends to other real numbers through analytic continuation.

For positive integers, Γ(n) = (n-1)!

Syntax

GAMMA(<x>)

Parameters

Parameter Description
<x> The input value for which to compute the Gamma function

Return Value

Returns a value of type DOUBLE. Special cases:

  • If the parameter is NULL, returns NULL
  • If the parameter is a positive integer n, returns (n-1)!
  • If the parameter is 0 or a negative integer, returns NaN
  • For very large positive values, may return Infinity

Examples

SELECT gamma(5);
+----------+
| gamma(5) |
+----------+
|       24 |
+----------+

SELECT gamma(3.5);
+--------------------+
| gamma(3.5)         |
+--------------------+
| 3.3233509704478426 |
+--------------------+

SELECT gamma(0.5);
+--------------------+
| gamma(0.5)         |
+--------------------+
| 1.7724538509055159 |
+--------------------+

SELECT gamma(-1);
+-----------+
| gamma(-1) |
+-----------+
|       nan |
+-----------+