Gamma

Gamma is the third letter of the Greek alphabet and is commonly denoted by the symbol gamma (uppercase Γ, lowercase γ). In science and mathematics it is used as a variable name and to label various functions and constants.

In mathematics, the gamma function extends the factorial to non-integer arguments. It is defined by Γ(z) = ∫_0^∞ t^{z-1} e^{-t} dt for Re(z) > 0 and satisfies Γ(z+1) = z Γ(z). For positive integers n, Γ(n) = (n-1)!.

The gamma distribution in probability theory uses the gamma function in its normalization; it has two parameters, shape k and scale θ (or shape α and rate β). Its density is f(x) = x^{k-1} e^{-x/θ} / (Γ(k) θ^k) for x>0.

In physics, gamma rays are high-energy photons produced by nuclear transitions and certain particle interactions; they form part of the electromagnetic spectrum beyond X-rays.

In astronomy, gamma-ray bursts are brief, extremely luminous events observed in distant galaxies, emitting most of their energy in the gamma-ray spectrum.

In computing and imaging, gamma refers to gamma correction, a nonlinear mapping applied to image luminance to account for human perception and display characteristics; typical gamma values around 2.2.