This is documentation for Mathematica 3, which was
based on an earlier version of the Wolfram Language.
 Gamma Gamma[ z ] is the Euler gamma function . Gamma[ a , z ] is the incomplete gamma function . Gamma[ a , , ] is the generalized incomplete gamma function . Mathematical function (see Section A.3.10). The gamma function satisfies . The incomplete gamma function satisfies . The generalized incomplete gamma function is given by the integral . Note that the arguments in the incomplete form of Gamma are arranged differently from those in the incomplete form of Beta. Gamma[ z ] has no branch cut discontinuities. Gamma[ a , z ] has a branch cut discontinuity in the complex z plane running from to . See the Mathematica book: Section 3.2.10. See also Implementation NotesA.9.44.15MainBookLinkOldButtonDataA.9.44.15. See also: Factorial, LogGamma, InverseGammaRegularized, PolyGamma, RiemannSiegelTheta. Further Examples Here are the first 10 integer values of the gamma function; these are the factorials offset by 1. In[1]:= Out[1]= The gamma function generalizes factorials to numbers beyond the positive integers. In[2]:= Out[2]= This is the derivative. In[3]:= Out[3]= This is a series expansion around . In[4]:= Out[4]=