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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.al7x.01

 Input Form

 Hypergeometric2F1[9/4, 7/2, 5, z] == -((512 Sqrt[2] (2 (1 + Sqrt[1 - z]) (1 - z)^(1/4) (192 - 176 z + 5 z^2) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (192 (1 + (1 - z)^(1/4) + Sqrt[1 - z] + (1 - z)^(3/4)) - 16 (17 + 11 (1 - z)^(1/4) + 11 Sqrt[1 - z] + 11 (1 - z)^(3/4)) z + 5 (15 + (1 - z)^(1/4) + Sqrt[1 - z] + (1 - z)^(3/4)) z^2 + 5 z^3) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)]))/ (525 Pi Sqrt[1 + Sqrt[1 - z]] (-1 + z) z^4))

 Standard Form

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 MathML Form

 2 F 1 ( 9 4 , 7 2 ; 5 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["9", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["7", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox["5", 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] - ( 512 2 ( 2 ( 1 - z + 1 ) 1 - z 4 ( 5 z 2 - 176 z + 192 ) E ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) - ( 5 z 3 + 5 ( ( 1 - z ) 3 / 4 + 1 - z + 1 - z 4 + 15 ) z 2 - 16 ( 11 ( 1 - z ) 3 / 4 + 11 1 - z + 11 1 - z 4 + 17 ) z + 192 ( ( 1 - z ) 3 / 4 + 1 - z + 1 - z 4 + 1 ) ) K ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) ) ) / ( 525 π 1 - z + 1 ( z - 1 ) z 4 ) HypergeometricPFQ 9 4 7 2 5 z -1 512 2 1 2 2 1 -1 z 1 2 1 1 -1 z 1 4 5 z 2 -1 176 z 192 EllipticE 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 -1 5 z 3 5 1 -1 z 3 4 1 -1 z 1 2 1 -1 z 1 4 15 z 2 -1 16 11 1 -1 z 3 4 11 1 -1 z 1 2 11 1 -1 z 1 4 17 z 192 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 -1 525 1 -1 z 1 2 1 1 2 z -1 z 4 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["9", "4"], ",", FractionBox["7", "2"], ",", "5", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List["512", " ", 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["192", "-", RowBox[List["176", " ", "z"]], "+", RowBox[List["5", " ", 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["192", " ", 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["16", " ", RowBox[List["(", RowBox[List["17", "+", RowBox[List["11", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]], "+", RowBox[List["11", " ", SqrtBox[RowBox[List["1", "-", "z"]]]]], "+", RowBox[List["11", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["3", "/", "4"]]]]]]], ")"]], " ", "z"]], "+", RowBox[List["5", " ", RowBox[List["(", RowBox[List["15", "+", 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"]]]]], ")"]], " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["5", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", 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["525", " ", "\[Pi]", " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", SuperscriptBox["z", "4"]]]]]]]]]]

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

 2007-05-02