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 BetaRegularized

 http://functions.wolfram.com/06.21.06.0037.01

 Input Form

 BetaRegularized[z, a, b] == ((z^a Gamma[a + b])/Gamma[b]) Hypergeometric2F1Regularized[a, 1 - b, a + 1, z]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["BetaRegularized", "[", RowBox[List["z", ",", "a", ",", "b"]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["z", "a"], RowBox[List["Gamma", "[", RowBox[List["a", "+", "b"]], "]"]]]], RowBox[List["Gamma", "[", "b", "]"]]], RowBox[List["Hypergeometric2F1Regularized", "[", RowBox[List["a", ",", RowBox[List["1", "-", "b"]], ",", RowBox[List["a", "+", "1"]], ",", "z"]], "]"]]]]]]]]

 MathML Form

 I BetaRegularized z ( a , b ) z a Γ ( a + b ) Γ ( b ) 2 F ~ 1 ( a , 1 - b ; a + 1 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox[OverscriptBox["F", "~"], FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["a", Hypergeometric2F1Regularized, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", "b"]], Hypergeometric2F1Regularized, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1Regularized, Rule[Editable, False]], ";", TagBox[TagBox[TagBox[RowBox[List["a", "+", "1"]], Hypergeometric2F1Regularized, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1Regularized, Rule[Editable, False]], ";", TagBox["z", Hypergeometric2F1Regularized, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQRegularized[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], Hypergeometric2F1Regularized] BetaRegularized z a b z a Gamma a b Gamma b -1 Hypergeometric2F1Regularized a 1 -1 b a 1 z [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["BetaRegularized", "[", RowBox[List["z_", ",", "a_", ",", "b_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["z", "a"], " ", RowBox[List["Gamma", "[", RowBox[List["a", "+", "b"]], "]"]]]], ")"]], " ", RowBox[List["Hypergeometric2F1Regularized", "[", RowBox[List["a", ",", RowBox[List["1", "-", "b"]], ",", RowBox[List["a", "+", "1"]], ",", "z"]], "]"]]]], RowBox[List["Gamma", "[", "b", "]"]]]]]]]

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

 2007-05-02