Mathematica 9 is now available
 Documentation / Mathematica / Built-in Functions / Mathematical Functions / Hypergeometric Related /
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]=



    Any questions about topics on this page? Click here to get an individual response.Buy NowMore Information
    THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT.
    SEE THE DOCUMENTATION CENTER FOR THE LATEST INFORMATION.