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: BetaRegularized, InverseBetaRegularized.