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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.ad0e.01

 Input Form

 Hypergeometric2F1[-(11/4), -(7/4), 1/4, z] == (1/1024) (8 (1 - z)^(3/4) (128 + 943 z + 84 z^2) - 462 Sqrt[2] z^(3/4) (7 + 8 z) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))] - 462 Sqrt[2] z^(3/4) (7 + 8 z) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))] - 231 Sqrt[2] z^(3/4) (7 + 8 z) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]] + 231 Sqrt[2] z^(3/4) (7 + 8 z) Log[1 + (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]])

 Standard Form

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 MathML Form

 2 F 1 ( - 11 4 , - 7 4 ; 1 4 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["-", FractionBox["11", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["-", FractionBox["7", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["1", "4"], 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] 1 1024 ( 8 ( 1 - z ) 3 / 4 ( 84 z 2 + 943 z + 128 ) - 462 2 z 3 / 4 ( 8 z + 7 ) tan - 1 ( 1 - z 4 2 1 - z 4 , - z 4 2 1 - z 4 ) - 462 2 z 3 / 4 ( 8 z + 7 ) tan - 1 ( z 4 2 1 - z 4 + 1 , - z 4 2 1 - z 4 ) - 231 2 z 3 / 4 ( 8 z + 7 ) log ( z 1 - z - 2 z 4 1 - z 4 + 1 ) + 231 2 z 3 / 4 ( 8 z + 7 ) log ( z 1 - z + 2 z 4 1 - z 4 + 1 ) ) HypergeometricPFQ -1 11 4 -1 7 4 1 4 z 1 1024 8 1 -1 z 3 4 84 z 2 943 z 128 -1 462 2 1 2 z 3 4 8 z 7 1 -1 z 1 4 2 1 2 1 -1 z 1 4 -1 -1 z 1 4 2 1 2 1 -1 z 1 4 -1 -1 462 2 1 2 z 3 4 8 z 7 z 1 4 2 1 2 1 -1 z 1 4 -1 1 -1 z 1 4 2 1 2 1 -1 z 1 4 -1 -1 231 2 1 2 z 3 4 8 z 7 z 1 2 1 -1 z 1 2 -1 -1 2 1 2 z 1 4 1 -1 z 1 4 -1 1 231 2 1 2 z 3 4 8 z 7 z 1 2 1 -1 z 1 2 -1 2 1 2 z 1 4 1 -1 z 1 4 -1 1 [/itex]

 Rule Form

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

 2007-05-02