Beta[a, b]
gives the Euler beta function .

Beta[z, a, b]
gives the incomplete beta function .


  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • .
  • .
  • Beta[z, a, b] has a branch cut discontinuity in the complex plane running from to .
  • Beta[z0, z1, 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.
  • For certain special arguments, Beta automatically evaluates to exact values.
  • Beta can be evaluated to arbitrary numerical precision.
  • Beta automatically threads over lists.
  • In TraditionalForm, Beta is output using \[CapitalBeta].
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