TeXipedia

varGamma

Represents an uppercase gamma variant commonly used in mathematical notation, particularly for special functions and operators.

Overview

Serves as a stylistic variant of the uppercase Gamma letter, offering a more cursive or flowing appearance compared to the standard uppercase Gamma.

  • Frequently appears in mathematical physics and complex analysis
  • Often used to denote special mathematical functions or operators
  • Particularly common in contexts involving gamma functions and their generalizations
  • Provides visual distinction when multiple Gamma-like symbols are needed in the same expression

Examples

Using the variant Gamma in a mathematical physics equation for the gamma function.

Γ(z)=∫0∞tz−1e−t dt\varGamma(z) = \int_0^\infty t^{z-1}e^{-t}\,dt 
\varGamma(z) = \int_0^\infty t^{z-1}e^{-t}\,dt

Representing a phase space boundary in statistical mechanics.

∮Γp dq=nh\oint_{\varGamma} p\,dq = nh 
\oint_{\varGamma} p\,dq = nh

Denoting a special curve in complex analysis.

∫Γf(z) dz=2πi∑k=1nRes(f,zk)\int_{\varGamma} f(z)\,dz = 2\pi i\sum_{k=1}^n \text{Res}(f,z_k) 
\int_{\varGamma} f(z)\,dz = 2\pi i\sum_{k=1}^n \text{Res}(f,z_k)