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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.azg1.01

 Input Form

 Hypergeometric2F1[1, 5, -(27/5), z] == (4194304 ((1 - z)^(4/5) - (1 - z)^(3/5) z^(1/5) + (1 - z)^(2/5) z^(2/5) - (1 - z)^(1/5) z^(3/5) + z^(4/5))^10 (-3155625 + 37633750 z - 209684375 z^2 + 733412500 z^3 - 1860184375 z^4 + 4007273750 z^5 - 13308195625 z^6 - 2585141856 z^7 + 466998840 z^8 - 67993200 z^9 + 5049000 z^10))/(3155625 ((1 - z)^(1/5) + z^(1/5)) (2 (1 - z)^(2/5) + (-1 + Sqrt[5]) (1 - z)^(1/5) z^(1/5) + 2 z^(2/5))^11 (2 (1 - z)^(2/5) - (1 + Sqrt[5]) (1 - z)^(1/5) z^(1/5) + 2 z^(2/5))^11 (-1 + z)^11) + (2531984 Sqrt[10 - 2 Sqrt[5]] z^(32/5) ArcTan[1 - ((1 - Sqrt[5]) z^(1/5))/(4 (1 - z)^(1/5)), -((Sqrt[5/8 + Sqrt[5]/8] z^(1/5))/(1 - z)^(1/5))])/ (3125 (1 - z)^(57/5)) - (2531984 Sqrt[2 (5 + Sqrt[5])] z^(32/5) ArcTan[1 - ((1 + Sqrt[5]) z^(1/5))/(4 (1 - z)^(1/5)), -((Sqrt[5/8 - Sqrt[5]/8] z^(1/5))/(1 - z)^(1/5))])/ (3125 (1 - z)^(57/5)) + (5063968 z^(32/5) Log[1 + z^(1/5)/(1 - z)^(1/5)])/ (3125 (1 - z)^(57/5)) - (1265992 (1 + Sqrt[5]) z^(32/5) Log[1 - ((1 - Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(3125 (1 - z)^(57/5)) + (1265992 (-1 + Sqrt[5]) z^(32/5) Log[1 - ((1 + Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(3125 (1 - z)^(57/5))

 Standard Form

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SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["2", "/", "5"]]]]]], "]"]]]], RowBox[List["3125", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["57", "/", "5"]]]]]], "+", FractionBox[RowBox[List["1265992", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox["5"]]], ")"]], " ", SuperscriptBox["z", RowBox[List["32", "/", "5"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["1", "+", SqrtBox["5"]]], ")"]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]], RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "5"]]]]]], "+", FractionBox[SuperscriptBox["z", RowBox[List["2", "/", "5"]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["2", "/", "5"]]]]]], "]"]]]], RowBox[List["3125", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], 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 MathML Form

 2 F 1 ( 1 , 5 ; - 27 5 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["1", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["5", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[RowBox[List["-", FractionBox["27", "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] ( 4194304 ( 5049000 z 10 - 67993200 z 9 + 466998840 z 8 - 2585141856 z 7 - 13308195625 z 6 + 4007273750 z 5 - 1860184375 z 4 + 733412500 z 3 - 209684375 z 2 + 37633750 z - 3155625 ) ( ( 1 - z ) 4 / 5 - z 5 ( 1 - z ) 3 / 5 + z 2 / 5 ( 1 - z ) 2 / 5 - z 3 / 5 1 - z 5 + z 4 / 5 ) 10 ) / ( 3155625 ( 1 - z 5 + z 5 ) ( 2 ( 1 - z ) 2 / 5 + ( - 1 + 5 ) z 5 1 - z 5 + 2 z 2 / 5 ) 11 ( 2 ( 1 - z ) 2 / 5 - ( 1 + 5 ) z 5 1 - z 5 + 2 z 2 / 5 ) 11 ( z - 1 ) 11 ) + 2531984 10 - 2 5 z 32 / 5 tan - 1 ( 1 - ( 1 - 5 ) z 5 4 1 - z 5 , - 5 8 + 5 8 z 5 1 - z 5 ) 3125 ( 1 - z ) 57 / 5 - 2531984 2 ( 5 + 5 ) z 32 / 5 tan - 1 ( 1 - ( 1 + 5 ) z 5 4 1 - z 5 , - 5 8 - 5 8 z 5 1 - z 5 ) 3125 ( 1 - z ) 57 / 5 + 5063968 z 32 / 5 log ( z 5 1 - z 5 + 1 ) 3125 ( 1 - z ) 57 / 5 - 1265992 ( 1 + 5 ) z 32 / 5 log ( z 2 / 5 ( 1 - z ) 2 / 5 - ( 1 - 5 ) z 5 2 1 - z 5 + 1 ) 3125 ( 1 - z ) 57 / 5 + 1265992 ( - 1 + 5 ) z 32 / 5 log ( z 2 / 5 ( 1 - z ) 2 / 5 - ( 1 + 5 ) z 5 2 1 - z 5 + 1 ) 3125 ( 1 - z ) 57 / 5 HypergeometricPFQ 1 5 -1 27 5 z 4194304 5049000 z 10 -1 67993200 z 9 466998840 z 8 -1 2585141856 z 7 -1 13308195625 z 6 4007273750 z 5 -1 1860184375 z 4 733412500 z 3 -1 209684375 z 2 37633750 z -3155625 1 -1 z 4 5 -1 z 1 5 1 -1 z 3 5 z 2 5 1 -1 z 2 5 -1 z 3 5 1 -1 z 1 5 z 4 5 10 3155625 1 -1 z 1 5 z 1 5 2 1 -1 z 2 5 -1 5 1 2 z 1 5 1 -1 z 1 5 2 z 2 5 11 2 1 -1 z 2 5 -1 1 5 1 2 z 1 5 1 -1 z 1 5 2 z 2 5 11 z -1 11 -1 2531984 10 -1 2 5 1 2 1 2 z 32 5 1 -1 1 -1 5 1 2 z 1 5 4 1 -1 z 1 5 -1 -1 5 8 5 1 2 8 -1 1 2 z 1 5 1 -1 z 1 5 -1 3125 1 -1 z 57 5 -1 -1 2531984 2 5 5 1 2 1 2 z 32 5 1 -1 1 5 1 2 z 1 5 4 1 -1 z 1 5 -1 -1 5 8 -1 5 1 2 8 -1 1 2 z 1 5 1 -1 z 1 5 -1 3125 1 -1 z 57 5 -1 5063968 z 32 5 z 1 5 1 -1 z 1 5 -1 1 3125 1 -1 z 57 5 -1 -1 1265992 1 5 1 2 z 32 5 z 2 5 1 -1 z 2 5 -1 -1 1 -1 5 1 2 z 1 5 2 1 -1 z 1 5 -1 1 3125 1 -1 z 57 5 -1 1265992 -1 5 1 2 z 32 5 z 2 5 1 -1 z 2 5 -1 -1 1 5 1 2 z 1 5 2 1 -1 z 1 5 -1 1 3125 1 -1 z 57 5 -1 [/itex]

 Rule Form

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

 2007-05-02