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 Beta

 http://functions.wolfram.com/06.19.07.0001.01

 Input Form

 Beta[z, a, b] == Integrate[t^(a - 1) (1 - t)^(b - 1), {t, 0, z}] /; Re[a] > 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Beta", "[", RowBox[List["z", ",", "a", ",", "b"]], "]"]], "\[Equal]", RowBox[List[SubsuperscriptBox["\[Integral]", "0", "z"], RowBox[List[SuperscriptBox["t", RowBox[List["a", "-", "1"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "t"]], ")"]], RowBox[List["b", "-", "1"]]], " ", RowBox[List["\[DifferentialD]", "t"]]]]]]]], "/;", RowBox[List[RowBox[List["Re", "[", "a", "]"]], ">", "0"]]]]]]

 MathML Form

 Β Beta z ( a , b ) 0 z t a - 1 ( 1 - t ) b - 1 t /; Re ( a ) > 0 Condition Beta z a b t 0 z t a -1 1 -1 t b -1 a 0 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Beta", "[", RowBox[List["z_", ",", "a_", ",", "b_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SubsuperscriptBox["\[Integral]", "0", "z"], RowBox[List[RowBox[List[SuperscriptBox["t", RowBox[List["a", "-", "1"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "t"]], ")"]], RowBox[List["b", "-", "1"]]]]], RowBox[List["\[DifferentialD]", "t"]]]]]], "/;", RowBox[List[RowBox[List["Re", "[", "a", "]"]], ">", "0"]]]]]]]]

 Date Added to functions.wolfram.com (modification date)

 2001-10-29