# Name of the Gamma function

The Gamma function for positive arguments can be defined with the integral

$$\Gamma(\alpha) = \int_0^\infty x^{\alpha-1} e^{-x}\,dx$$

The function $x^{\alpha-1} e^{-x}$ is called the Gamma distribution when normalized.

How are the two names related?

• Did the Gamma function get this name and the $\Gamma$ symbol because the distribution was already called Gamma distribution?
• Or backwards, did the Gamma distribution get named from the Gamma function?
• Or were the two named together at the same time?
• Or are the two names independent and only accidentally the same letter, despite the apparent connection?

This question came up in a discussion about spelling mathematical terms, and while it's probably not actually relevant for that, I'm now curious about the origin of the names.