gamma function
noun
A function (symbol Γ) which extends the notion of factorial n (written n!) from positive whole numbers to real and complex variables, given by Γ(z) = ∫∞ 0 t z − 1 e −t dt.
- The function has the properties that Γ(z) = (z − 1)!, and Γ(z + 1) = zΓ(z), and is undefined for values of z that are negative whole numbers or zero. The incomplete gamma function is obtained by varying one or other of the limits of integration in the defining equation.The function was devised by Euler in 1729 (L. Euler Let. 13 Oct. 1729, in P. H. Fuss Correspondance mathématique et physique (1843) I. 3–4), but not named by him; the name and symbol Γ were given by Legendre in 1809 (Mém. de la classe des sci. mathématiques et physiques de l'Inst. de France, année 1809 (1810) 477; also A. M. Legendre Exercises de calcul intégral (1811) I. ii. 277)..
Origin
Mid 19th century; earliest use found in Reports of the British Association for the Advancement of Science.