# gamma function

(30 minutes to learn)

## Summary

The gamma function is a generalization of factorials to real and complex numbers, e.g. 5.25! isn't well defined, but Gamma(5.25) is well defined. The Gamma function is formally defined as an improper integral that converges. It appears in a number of common distributions, e.g. the beta, gamma, and Dirichlet distribution.

## Context

-this concept has no prerequisites-

## Core resources (read/watch one of the following)

## -Paid-

→ The Princeton Companion to Mathematics (2008)

A surprisingly readable and comprehensive reference on the major topics in pure math.

Location:
Section 3.31, "The gamma function," pages 213-214

## Supplemental resources (the following are optional, but you may find them useful)

## -Free-

→ Wikipedia

→ Wolfram MathWorld

## -Paid-

→ Probability and Statistics

An introductory textbook on probability theory and statistics.

Location:
Definition 5.7.1 (p. 317)

## See also

- The gamma function can be approximated with Stirling's formula .
- The gamma function features centrally in the Riemann hypothesis .
- The gamma function is needed to define several probability distributions: The gamma function is an example of an analytic function .