TeXipedia

Gamma

Represents a capital gamma letter commonly used in mathematics and physics to denote special functions, surface boundaries, or mathematical constants.

Overview

Essential in advanced mathematics and theoretical physics, serving multiple distinct purposes across different domains.

  • Frequently used to represent the gamma function, a fundamental special function extending factorial operations to complex numbers.
  • In physics and engineering, often denotes decay constants, reflection coefficients, or surface boundaries in geometric problems.
  • Common in statistical mechanics and quantum field theory for describing particle interactions and state spaces.
  • Appears regularly in mathematical proofs and theoretical frameworks where Greek letters denote specific mathematical objects or functions.

Examples

Definition of the Gamma function for positive real numbers.

Γ(n)=(n−1)!\Gamma(n) = (n-1)! 
\Gamma(n) = (n-1)!

Representation of a boundary in mathematical physics.

∂u∂n∣Γ=0\frac{\partial u}{\partial n}\bigg|_{\Gamma} = 0 
\frac{\partial u}{\partial n}\bigg|_{\Gamma} = 0

Matrix notation in linear algebra.

Γ=(abcd)\Gamma = \begin{pmatrix} a & b \\ c & d \end{pmatrix} 
\Gamma = \begin{pmatrix} a & b \\ c & d \end{pmatrix}