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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.aljw.01

 Input Form

 Hypergeometric2F1[5/2, 13/4, 3, z] == -((16 Sqrt[2] (2 (1 + Sqrt[1 - z]) (1 - z)^(1/4) (-4 + 13 z + 12 z^2) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (-4 (1 + (1 - z)^(1/4) + Sqrt[1 - z] + (1 - z)^(3/4)) + (15 + 13 (1 - z)^(1/4) + 13 Sqrt[1 - z] + 13 (1 - z)^(3/4)) z + (-11 + 12 (1 - z)^(1/4) + 12 Sqrt[1 - z] + 12 (1 - z)^(3/4)) z^2) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)]))/ (135 Pi Sqrt[1 + Sqrt[1 - z]] (-1 + z)^3 z^2))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["5", "2"], ",", FractionBox["13", "4"], ",", "3", ",", "z"]], "]"]], "\[Equal]", RowBox[List["-", RowBox[List[RowBox[List["(", RowBox[List["16", " ", SqrtBox["2"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", RowBox[List["(", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "4"]], "+", RowBox[List["13", " ", "z"]], "+", RowBox[List["12", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", FractionBox[RowBox[List[RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]], "+", "z"]], RowBox[List["2", " ", "z"]]], "]"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "4"]], " ", RowBox[List["(", RowBox[List["1", "+", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], "+", SqrtBox[RowBox[List["1", "-", "z"]]], "+", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["3", "/", "4"]]]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["15", "+", RowBox[List["13", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]], "+", RowBox[List["13", " ", SqrtBox[RowBox[List["1", "-", "z"]]]]], "+", RowBox[List["13", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["3", "/", "4"]]]]]]], ")"]], " ", "z"]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "11"]], "+", RowBox[List["12", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]], "+", RowBox[List["12", " ", SqrtBox[RowBox[List["1", "-", "z"]]]]], "+", RowBox[List["12", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["3", "/", "4"]]]]]]], ")"]], " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", FractionBox[RowBox[List[RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]], "+", "z"]], RowBox[List["2", " ", "z"]]], "]"]]]]]], ")"]]]], ")"]], "/", RowBox[List["(", RowBox[List["135", " ", "\[Pi]", " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "3"], " ", SuperscriptBox["z", "2"]]], ")"]]]]]]]]]]

 MathML Form

 2 F 1 ( 5 2 , 13 4 ; 3 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["5", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["13", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox["3", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox["z", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQ] - ( 16 2 ( 2 ( 1 - z + 1 ) 1 - z 4 ( 12 z 2 + 13 z - 4 ) E ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) - ( ( 12 ( 1 - z ) 3 / 4 + 12 1 - z + 12 1 - z 4 - 11 ) z 2 + ( 13 ( 1 - z ) 3 / 4 + 13 1 - z + 13 1 - z 4 + 15 ) z - 4 ( ( 1 - z ) 3 / 4 + 1 - z + 1 - z 4 + 1 ) ) K ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) ) ) / ( 135 π 1 - z + 1 ( z - 1 ) 3 z 2 ) HypergeometricPFQ 5 2 13 4 3 z -1 16 2 1 2 2 1 -1 z 1 2 1 1 -1 z 1 4 12 z 2 13 z -4 EllipticE 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 -1 12 1 -1 z 3 4 12 1 -1 z 1 2 12 1 -1 z 1 4 -11 z 2 13 1 -1 z 3 4 13 1 -1 z 1 2 13 1 -1 z 1 4 15 z -1 4 1 -1 z 3 4 1 -1 z 1 2 1 -1 z 1 4 1 EllipticK 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 135 1 -1 z 1 2 1 1 2 z -1 3 z 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["5", "2"], ",", FractionBox["13", "4"], ",", "3", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List["16", " ", SqrtBox["2"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", RowBox[List["(", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "4"]], "+", RowBox[List["13", " ", "z"]], "+", RowBox[List["12", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", FractionBox[RowBox[List[RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]], "+", "z"]], RowBox[List["2", " ", "z"]]], "]"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "4"]], " ", RowBox[List["(", RowBox[List["1", "+", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], "+", SqrtBox[RowBox[List["1", "-", "z"]]], "+", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["3", "/", "4"]]]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["15", "+", RowBox[List["13", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]], "+", RowBox[List["13", " ", SqrtBox[RowBox[List["1", "-", "z"]]]]], "+", RowBox[List["13", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["3", "/", "4"]]]]]]], ")"]], " ", "z"]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "11"]], "+", RowBox[List["12", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]], "+", RowBox[List["12", " ", SqrtBox[RowBox[List["1", "-", "z"]]]]], "+", RowBox[List["12", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["3", "/", "4"]]]]]]], ")"]], " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", FractionBox[RowBox[List[RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]], "+", "z"]], RowBox[List["2", " ", "z"]]], "]"]]]]]], ")"]]]], RowBox[List["135", " ", "\[Pi]", " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "3"], " ", SuperscriptBox["z", "2"]]]]]]]]]]

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

 2007-05-02