Gamma

How to read it

Gamma is said GAM-uh (/ˈɡæm.ə/ in both British and American English, Cambridge Dictionary). Modern Greek γάμμα has no hard g: the University of Arizona’s guide spells it “Ghamma”, with a throaty gh like the Arabic غ, closer to a y before the “soft” vowels.

Also searched as: gamma letter, gamma symbol, γ, Γ, γ meaning.

Capital, small and look-alike forms

Unicode’s chart notes “gamma function” beside the capital Γ, and cross-refers the small γ to the Latin small letter gamma ɣ (U+0263), a separate character that looks like it.

Gamma in maths

Γ(z) is the gamma function, which NIST’s Digital Library of Mathematical Functions defines by Euler’s integral. Jeff Miller’s history of mathematical symbols says Adrien-Marie Legendre introduced the letter Γ for it, and that why he chose that letter is unknown. The same library defines the small γ as Euler’s constant, 0.57721 56649 01532 86060…. Who first wrote γ for the constant is disputed in Miller’s sources: William Dunham credits Mascheroni, the CRC Concise Encyclopedia of Mathematics says Euler used it in 1781, and Julio González Cabillón found it in an 1835 essay by Carl Anton Bretschneider.

In AI and machine learning

In reinforcement learning, γ is the discount factor. Google’s Machine Learning Glossary writes an episode’s return as r₀ + γr₁ + γ²r₂ + …, so each reward further in the future is discounted once more. PyTorch uses γ for something else: its optimisers list “γ (lr)”, the learning rate, where Stanford’s CS229 notes write α and scikit-learn’s guide writes η. In batch normalisation, γ is the learnable scale that multiplies each normalised value, and β the shift (PyTorch documentation).

In quantum physics

γ is the photon. OpenStax’s University Physics gives gamma as the photon’s symbol in its table of particles, and says gamma rays are high-energy photons.

Other uses of gamma

Gamma rays are the third of the kinds of nuclear radiation early experimenters named alpha, beta and gamma (OpenStax). In relativity γ is the Lorentz factor, γ = 1/√(1 − v²/c²), by which a moving clock’s time is dilated (OpenStax). The American Heritage Dictionary also lists gamma as an old unit of mass, one millionth of a gram, and of magnetic intensity, one hundred-thousandth of an oersted.