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 Documentation / Mathematica / Built-in Functions / Mathematical Functions / Hypergeometric Related  /
Beta

  • Beta[ a , b ] gives the Euler beta function .
  • Beta[ z , a , b ] gives the incomplete beta function .
  • Mathematical function (see Section A.3.10).
  • .
  • .
  • Beta[ z , a , b ] has a branch cut discontinuity in the complex z plane running from to .
  • Beta[ , , a , b ] gives the generalized incomplete beta function .
  • Note that the arguments in the incomplete form of Beta are arranged differently from those in the incomplete form of Gamma.
  • In TraditionalForm, Beta is output using \[CapitalBeta].
  • See the Mathematica book: Section 3.2.10.
  • See also: InverseBetaRegularized.

    Further Examples

    Here is a symbolic result.

    In[1]:=

    Out[1]=

    This is the derivative.

    In[2]:=

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    This is the second derivative.

    In[3]:=

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    For a and b positive real, this just gives an alternate definition of the Beta function.

    In[4]:=

    Out[4]=

    In[5]:=

    Out[5]=