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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.b2gl.01

 Input Form

 Hypergeometric2F1[3, 4, 8/5, z] == -((2929 + 4750 z + 175 z^2)/(3125 (-1 + z)^5)) + (42 Sqrt[10 - 2 Sqrt[5]] (7 + 105 z + 75 z^2) 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))])/ (15625 (1 - z)^(27/5) z^(3/5)) - (42 Sqrt[2 (5 + Sqrt[5])] (7 + 105 z + 75 z^2) 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))])/ (15625 (1 - z)^(27/5) z^(3/5)) + (84 (7 + 105 z + 75 z^2) Log[1 + z^(1/5)/(1 - z)^(1/5)])/ (15625 (1 - z)^(27/5) z^(3/5)) - (21 (1 + Sqrt[5]) (7 + 105 z + 75 z^2) Log[1 - ((1 - Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(15625 (1 - z)^(27/5) z^(3/5)) + (21 (-1 + Sqrt[5]) (7 + 105 z + 75 z^2) Log[1 - ((1 + Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(15625 (1 - z)^(27/5) z^(3/5))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List["3", ",", "4", ",", FractionBox["8", "5"], ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["2929", "+", RowBox[List["4750", " ", "z"]], "+", RowBox[List["175", " ", SuperscriptBox["z", "2"]]]]], RowBox[List["3125", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "5"]]]]]], "+", FractionBox[RowBox[List["42", " ", SqrtBox[RowBox[List["10", "-", RowBox[List["2", " ", SqrtBox["5"]]]]]], " ", RowBox[List["(", RowBox[List["7", "+", RowBox[List["105", " ", "z"]], "+", RowBox[List["75", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["ArcTan", "[", RowBox[List[RowBox[List["1", "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["1", "-", SqrtBox["5"]]], ")"]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]], RowBox[List["4", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", 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SuperscriptBox["z", RowBox[List["3", "/", "5"]]]]]]]]]]]]

 MathML Form

 2 F 1 ( 3 , 4 ; 8 5 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["3", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["4", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["8", "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] - 175 z 2 + 4750 z + 2929 3125 ( z - 1 ) 5 + 42 10 - 2 5 ( 75 z 2 + 105 z + 7 ) tan - 1 ( 1 - ( 1 - 5 ) z 5 4 1 - z 5 , - 5 8 + 5 8 z 5 1 - z 5 ) 15625 ( 1 - z ) 27 / 5 z 3 / 5 - 42 2 ( 5 + 5 ) ( 75 z 2 + 105 z + 7 ) tan - 1 ( 1 - ( 1 + 5 ) z 5 4 1 - z 5 , - 5 8 - 5 8 z 5 1 - z 5 ) 15625 ( 1 - z ) 27 / 5 z 3 / 5 + 84 ( 75 z 2 + 105 z + 7 ) log ( z 5 1 - z 5 + 1 ) 15625 ( 1 - z ) 27 / 5 z 3 / 5 - 21 ( 1 + 5 ) ( 75 z 2 + 105 z + 7 ) log ( z 2 / 5 ( 1 - z ) 2 / 5 - ( 1 - 5 ) z 5 2 1 - z 5 + 1 ) 15625 ( 1 - z ) 27 / 5 z 3 / 5 + 21 ( - 1 + 5 ) ( 75 z 2 + 105 z + 7 ) log ( z 2 / 5 ( 1 - z ) 2 / 5 - ( 1 + 5 ) z 5 2 1 - z 5 + 1 ) 15625 ( 1 - z ) 27 / 5 z 3 / 5 HypergeometricPFQ 3 4 8 5 z -1 175 z 2 4750 z 2929 3125 z -1 5 -1 42 10 -1 2 5 1 2 1 2 75 z 2 105 z 7 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 15625 1 -1 z 27 5 z 3 5 -1 -1 42 2 5 5 1 2 1 2 75 z 2 105 z 7 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 15625 1 -1 z 27 5 z 3 5 -1 84 75 z 2 105 z 7 z 1 5 1 -1 z 1 5 -1 1 15625 1 -1 z 27 5 z 3 5 -1 -1 21 1 5 1 2 75 z 2 105 z 7 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 15625 1 -1 z 27 5 z 3 5 -1 21 -1 5 1 2 75 z 2 105 z 7 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 15625 1 -1 z 27 5 z 3 5 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List["3", ",", "4", ",", FractionBox["8", "5"], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["2929", "+", RowBox[List["4750", " ", "z"]], "+", RowBox[List["175", " ", SuperscriptBox["z", "2"]]]]], RowBox[List["3125", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "5"]]]]]], "+", FractionBox[RowBox[List["42", " ", SqrtBox[RowBox[List["10", "-", RowBox[List["2", " ", SqrtBox["5"]]]]]], " ", RowBox[List["(", RowBox[List["7", "+", RowBox[List["105", " ", "z"]], "+", RowBox[List["75", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["ArcTan", "[", RowBox[List[RowBox[List["1", "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["1", "-", SqrtBox["5"]]], ")"]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]], RowBox[List["4", " ", SuperscriptBox[RowBox[List["(", 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 Date Added to functions.wolfram.com (modification date)

 2007-05-02