From 7baf12b74af590f9175778add7e6cf285fadabc6 Mon Sep 17 00:00:00 2001
From: tommyhugh2333-rgb <tommyhugh2333@gmail.com>
Date: Wed, 4 Feb 2026 16:40:00 +0800
Subject: [PATCH] [docs] Add documentation for GAMMA function

---
 .../numeric-functions/gamma.md                | 82 +++++++++++++++++++
 .../numeric-functions/gamma.md                | 82 +++++++++++++++++++
 2 files changed, 164 insertions(+)
 create mode 100644 docs/sql-manual/sql-functions/scalar-functions/numeric-functions/gamma.md
 create mode 100644 i18n/zh-CN/docusaurus-plugin-content-docs/current/sql-manual/sql-functions/scalar-functions/numeric-functions/gamma.md

diff --git a/docs/sql-manual/sql-functions/scalar-functions/numeric-functions/gamma.md b/docs/sql-manual/sql-functions/scalar-functions/numeric-functions/gamma.md
new file mode 100644
index 0000000000000..afe8bc81c8ad9
--- /dev/null
+++ b/docs/sql-manual/sql-functions/scalar-functions/numeric-functions/gamma.md
@@ -0,0 +1,82 @@
+---
+{
+    "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
+
+```sql
+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
+
+```sql
+SELECT gamma(5);
+```
+
+```text
++----------+
+| gamma(5) |
++----------+
+|       24 |
++----------+
+```
+
+```sql
+SELECT gamma(3.5);
+```
+
+```text
++--------------------+
+| gamma(3.5)         |
++--------------------+
+| 3.3233509704478426 |
++--------------------+
+```
+
+```sql
+SELECT gamma(0.5);
+```
+
+```text
++--------------------+
+| gamma(0.5)         |
++--------------------+
+| 1.7724538509055159 |
++--------------------+
+```
+
+```sql
+SELECT gamma(-1);
+```
+
+```text
++-----------+
+| gamma(-1) |
++-----------+
+|       nan |
++-----------+
\ No newline at end of file
diff --git a/i18n/zh-CN/docusaurus-plugin-content-docs/current/sql-manual/sql-functions/scalar-functions/numeric-functions/gamma.md b/i18n/zh-CN/docusaurus-plugin-content-docs/current/sql-manual/sql-functions/scalar-functions/numeric-functions/gamma.md
new file mode 100644
index 0000000000000..799d1aa46fcbf
--- /dev/null
+++ b/i18n/zh-CN/docusaurus-plugin-content-docs/current/sql-manual/sql-functions/scalar-functions/numeric-functions/gamma.md
@@ -0,0 +1,82 @@
+---
+{
+    "title": "GAMMA",
+    "language": "zh-CN",
+    "description": "返回 x 的 Gamma 函数值。"
+}
+---
+
+## 描述
+
+返回 `x` 的 Gamma 函数值。Gamma 函数定义为 `Γ(x) = ∫₀^∞ t^(x-1)e^(-t)dt`（当 x > 0），并通过解析延拓扩展到其他实数。
+
+对于正整数，`Γ(n) = (n-1)!`
+
+## 语法
+
+```sql
+GAMMA(<x>)
+```
+
+## 参数
+
+| 参数 | 说明 |
+| -- | -- |
+| `<x>` | 用于计算 Gamma 函数的输入值 |
+
+## 返回值
+
+返回一个 DOUBLE 类型的值。特殊情况：
+- 当参数为 NULL 时，返回 NULL
+- 当参数为正整数 n 时，返回 (n-1)!
+- 当参数为 0 或负整数时，返回 NaN
+- 对于非常大的正值，可能返回 Infinity
+
+## 举例
+
+```sql
+SELECT gamma(5);
+```
+
+```text
++----------+
+| gamma(5) |
++----------+
+|       24 |
++----------+
+```
+
+```sql
+SELECT gamma(3.5);
+```
+
+```text
++--------------------+
+| gamma(3.5)         |
++--------------------+
+| 3.3233509704478426 |
++--------------------+
+```
+
+```sql
+SELECT gamma(0.5);
+```
+
+```text
++--------------------+
+| gamma(0.5)         |
++--------------------+
+| 1.7724538509055159 |
++--------------------+
+```
+
+```sql
+SELECT gamma(-1);
+```
+
+```text
++-----------+
+| gamma(-1) |
++-----------+
+|       nan |
++-----------+
\ No newline at end of file