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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.a906.01

 Input Form

 Hypergeometric2F1[-(19/4), -(19/4), 5/4, z] == (1/2684354560) (184 (1 - z)^(3/4) (10401205 + 131331584 z + 277203408 z^2 + 128398592 z^3 + 9826816 z^4) - (1/z^(1/4)) (43890 Sqrt[2] (4389 + 146300 z + 668800 z^2 + 729600 z^3 + 194560 z^4 + 8192 z^5) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))]) - (1/z^(1/4)) (43890 Sqrt[2] (4389 + 146300 z + 668800 z^2 + 729600 z^3 + 194560 z^4 + 8192 z^5) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))]) - (1/z^(1/4)) (21945 Sqrt[2] (4389 + 146300 z + 668800 z^2 + 729600 z^3 + 194560 z^4 + 8192 z^5) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]]) + (1/z^(1/4)) (21945 Sqrt[2] (4389 + 146300 z + 668800 z^2 + 729600 z^3 + 194560 z^4 + 8192 z^5) 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 ; 5 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["5", "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 2684354560 ( 184 ( 1 - z ) 3 / 4 ( 9826816 z 4 + 128398592 z 3 + 277203408 z 2 + 131331584 z + 10401205 ) - 1 z 4 43890 2 ( 8192 z 5 + 194560 z 4 + 729600 z 3 + 668800 z 2 + 146300 z + 4389 ) tan - 1 ( 1 - z 4 2 1 - z 4 , - z 4 2 1 - z 4 ) - 1 z 4 43890 2 ( 8192 z 5 + 194560 z 4 + 729600 z 3 + 668800 z 2 + 146300 z + 4389 ) tan - 1 ( z 4 2 1 - z 4 + 1 , - z 4 2 1 - z 4 ) - 1 z 4 21945 2 ( 8192 z 5 + 194560 z 4 + 729600 z 3 + 668800 z 2 + 146300 z + 4389 ) log ( z 1 - z - 2 z 4 1 - z 4 + 1 ) + 1 z 4 21945 2 ( 8192 z 5 + 194560 z 4 + 729600 z 3 + 668800 z 2 + 146300 z + 4389 ) log ( z 1 - z + 2 z 4 1 - z 4 + 1 ) ) HypergeometricPFQ -1 19 4 -1 19 4 5 4 z 1 2684354560 184 1 -1 z 3 4 9826816 z 4 128398592 z 3 277203408 z 2 131331584 z 10401205 -1 1 z 1 4 -1 43890 2 1 2 8192 z 5 194560 z 4 729600 z 3 668800 z 2 146300 z 4389 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 1 z 1 4 -1 43890 2 1 2 8192 z 5 194560 z 4 729600 z 3 668800 z 2 146300 z 4389 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 1 z 1 4 -1 21945 2 1 2 8192 z 5 194560 z 4 729600 z 3 668800 z 2 146300 z 4389 z 1 2 1 -1 z 1 2 -1 -1 2 1 2 z 1 4 1 -1 z 1 4 -1 1 1 z 1 4 -1 21945 2 1 2 8192 z 5 194560 z 4 729600 z 3 668800 z 2 146300 z 4389 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