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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.a902.01

 Input Form

 Hypergeometric2F1[-(19/4), -(19/4), 1/4, z] == (1/33554432) (8 (1 - z)^(3/4) (4194304 + 221153989 z + 819815364 z^2 + 543491744 z^3 + 54257024 z^4) - 43890 Sqrt[2] z^(3/4) (7315 + 66880 z + 109440 z^2 + 38912 z^3 + 2048 z^4) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))] - 43890 Sqrt[2] z^(3/4) (7315 + 66880 z + 109440 z^2 + 38912 z^3 + 2048 z^4) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))] - 21945 Sqrt[2] z^(3/4) (7315 + 66880 z + 109440 z^2 + 38912 z^3 + 2048 z^4) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]] + 21945 Sqrt[2] z^(3/4) (7315 + 66880 z + 109440 z^2 + 38912 z^3 + 2048 z^4) 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 ( - 19 4 , - 19 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["19", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["-", FractionBox["19", "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 33554432 ( 8 ( 1 - z ) 3 / 4 ( 54257024 z 4 + 543491744 z 3 + 819815364 z 2 + 221153989 z + 4194304 ) - 43890 2 z 3 / 4 ( 2048 z 4 + 38912 z 3 + 109440 z 2 + 66880 z + 7315 ) tan - 1 ( 1 - z 4 2 1 - z 4 , - z 4 2 1 - z 4 ) - 43890 2 z 3 / 4 ( 2048 z 4 + 38912 z 3 + 109440 z 2 + 66880 z + 7315 ) tan - 1 ( z 4 2 1 - z 4 + 1 , - z 4 2 1 - z 4 ) - 21945 2 z 3 / 4 ( 2048 z 4 + 38912 z 3 + 109440 z 2 + 66880 z + 7315 ) log ( z 1 - z - 2 z 4 1 - z 4 + 1 ) + 21945 2 z 3 / 4 ( 2048 z 4 + 38912 z 3 + 109440 z 2 + 66880 z + 7315 ) log ( z 1 - z + 2 z 4 1 - z 4 + 1 ) ) HypergeometricPFQ -1 19 4 -1 19 4 1 4 z 1 33554432 8 1 -1 z 3 4 54257024 z 4 543491744 z 3 819815364 z 2 221153989 z 4194304 -1 43890 2 1 2 z 3 4 2048 z 4 38912 z 3 109440 z 2 66880 z 7315 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 43890 2 1 2 z 3 4 2048 z 4 38912 z 3 109440 z 2 66880 z 7315 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 21945 2 1 2 z 3 4 2048 z 4 38912 z 3 109440 z 2 66880 z 7315 z 1 2 1 -1 z 1 2 -1 -1 2 1 2 z 1 4 1 -1 z 1 4 -1 1 21945 2 1 2 z 3 4 2048 z 4 38912 z 3 109440 z 2 66880 z 7315 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