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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.b0ya.01

 Input Form

 Hypergeometric2F1[2, 3, -(16/5), z] == (11000 - 108625 z + 529250 z^2 - 1956000 z^3 + 17718750 z^4 + 10496289 z^5 + 120120 z^6)/(11000 (-1 + z)^8) - (8463 Sqrt[2 (5 + Sqrt[5])] z^(21/5) (13 + 5 z) 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))])/ (625 (1 - z)^(41/5)) - (8463 Sqrt[10 - 2 Sqrt[5]] z^(21/5) (13 + 5 z) 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))])/ (625 (1 - z)^(41/5)) - (16926 z^(21/5) (13 + 5 z) Log[1 + z^(1/5)/(1 - z)^(1/5)])/(625 (1 - z)^(41/5)) - (8463 (-1 + Sqrt[5]) z^(21/5) (13 + 5 z) Log[1 - ((1 - Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(1250 (1 - z)^(41/5)) + (8463 (1 + Sqrt[5]) z^(21/5) (13 + 5 z) Log[1 - ((1 + Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(1250 (1 - z)^(41/5))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List["2", ",", "3", ",", RowBox[List["-", FractionBox["16", "5"]]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["11000", "-", RowBox[List["108625", " ", "z"]], "+", RowBox[List["529250", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["1956000", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["17718750", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["10496289", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["120120", " ", SuperscriptBox["z", "6"]]]]], RowBox[List["11000", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "8"]]]], "-", FractionBox[RowBox[List["8463", " ", SqrtBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List["5", "+", SqrtBox["5"]]], ")"]]]]], " ", SuperscriptBox["z", RowBox[List["21", "/", "5"]]], " ", RowBox[List["(", RowBox[List["13", "+", RowBox[List["5", " ", "z"]]]], ")"]], " ", RowBox[List["ArcTan", "[", 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"z"]], ")"]], RowBox[List["41", "/", "5"]]]]]]]]]]]]

 MathML Form

 2 F 1 ( 2 , 3 ; - 16 5 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["2", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["3", 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["16", "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] - 8463 2 ( 5 + 5 ) ( 5 z + 13 ) tan - 1 ( 1 - ( 1 - 5 ) z 5 4 1 - z 5 , - 5 8 + 5 8 z 5 1 - z 5 ) z 21 / 5 625 ( 1 - z ) 41 / 5 - 8463 10 - 2 5 ( 5 z + 13 ) tan - 1 ( 1 - ( 1 + 5 ) z 5 4 1 - z 5 , - 5 8 - 5 8 z 5 1 - z 5 ) z 21 / 5 625 ( 1 - z ) 41 / 5 - 16926 ( 5 z + 13 ) log ( z 5 1 - z 5 + 1 ) z 21 / 5 625 ( 1 - z ) 41 / 5 - 8463 ( - 1 + 5 ) ( 5 z + 13 ) log ( z 2 / 5 ( 1 - z ) 2 / 5 - ( 1 - 5 ) z 5 2 1 - z 5 + 1 ) z 21 / 5 1250 ( 1 - z ) 41 / 5 + 8463 ( 1 + 5 ) ( 5 z + 13 ) log ( z 2 / 5 ( 1 - z ) 2 / 5 - ( 1 + 5 ) z 5 2 1 - z 5 + 1 ) z 21 / 5 1250 ( 1 - z ) 41 / 5 + 120120 z 6 + 10496289 z 5 + 17718750 z 4 - 1956000 z 3 + 529250 z 2 - 108625 z + 11000 11000 ( z - 1 ) 8 HypergeometricPFQ 2 3 -1 16 5 z -1 8463 2 5 5 1 2 1 2 5 z 13 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 z 21 5 625 1 -1 z 41 5 -1 -1 8463 10 -1 2 5 1 2 1 2 5 z 13 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 z 21 5 625 1 -1 z 41 5 -1 -1 16926 5 z 13 z 1 5 1 -1 z 1 5 -1 1 z 21 5 625 1 -1 z 41 5 -1 -1 8463 -1 5 1 2 5 z 13 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 z 21 5 1250 1 -1 z 41 5 -1 8463 1 5 1 2 5 z 13 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 z 21 5 1250 1 -1 z 41 5 -1 120120 z 6 10496289 z 5 17718750 z 4 -1 1956000 z 3 529250 z 2 -1 108625 z 11000 11000 z -1 8 -1 [/itex]

 Rule Form

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

 2007-05-02