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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.b0yb.01

 Input Form

 Hypergeometric2F1[2, 3, -(14/5), z] == (-2625 + 24000 z - 113250 z^2 + 497500 z^3 + 750677 z^4 + 23940 z^5)/ (2625 (-1 + z)^7) + (6612 Sqrt[2 (5 + Sqrt[5])] z^(19/5) (12 + 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)^(39/5)) + (6612 Sqrt[10 - 2 Sqrt[5]] z^(19/5) (12 + 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)^(39/5)) - (13224 z^(19/5) (12 + 5 z) Log[1 + z^(1/5)/(1 - z)^(1/5)])/(625 (1 - z)^(39/5)) - (3306 (-1 + Sqrt[5]) z^(19/5) (12 + 5 z) Log[1 - ((1 - Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(625 (1 - z)^(39/5)) + (3306 (1 + Sqrt[5]) z^(19/5) (12 + 5 z) Log[1 - ((1 + Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(625 (1 - z)^(39/5))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List["2", ",", "3", ",", RowBox[List["-", FractionBox["14", "5"]]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List[RowBox[List["-", "2625"]], "+", RowBox[List["24000", " ", "z"]], "-", RowBox[List["113250", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["497500", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["750677", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["23940", " ", SuperscriptBox["z", "5"]]]]], RowBox[List["2625", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "7"]]]], "+", FractionBox[RowBox[List["6612", " ", SqrtBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List["5", "+", SqrtBox["5"]]], ")"]]]]], " ", SuperscriptBox["z", RowBox[List["19", "/", "5"]]], " ", RowBox[List["(", RowBox[List["12", "+", RowBox[List["5", " ", "z"]]]], ")"]], " ", 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", "/", "5"]]]]]]]], ",", RowBox[List["-", FractionBox[RowBox[List[SqrtBox[RowBox[List[FractionBox["5", "8"], "+", FractionBox[SqrtBox["5"], "8"]]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "5"]]]]]]]], "]"]]]], RowBox[List["625", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["39", "/", "5"]]]]]], "+", FractionBox[RowBox[List["6612", " ", SqrtBox[RowBox[List["10", "-", RowBox[List["2", " ", SqrtBox["5"]]]]]], " ", SuperscriptBox["z", RowBox[List["19", "/", "5"]]], " ", RowBox[List["(", RowBox[List["12", "+", RowBox[List["5", " ", "z"]]]], ")"]], " ", 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", "/", "5"]]]]]]]], ",", RowBox[List["-", FractionBox[RowBox[List[SqrtBox[RowBox[List[FractionBox["5", "8"], "-", FractionBox[SqrtBox["5"], "8"]]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "5"]]]]]]]], "]"]]]], RowBox[List["625", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["39", "/", "5"]]]]]], "-", FractionBox[RowBox[List["13224", " ", SuperscriptBox["z", RowBox[List["19", "/", "5"]]], " ", RowBox[List["(", RowBox[List["12", "+", RowBox[List["5", " ", "z"]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", FractionBox[SuperscriptBox["z", RowBox[List["1", "/", "5"]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "5"]]]]]], "]"]]]], RowBox[List["625", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["39", "/", "5"]]]]]], "-", FractionBox[RowBox[List["3306", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox["5"]]], ")"]], " ", SuperscriptBox["z", RowBox[List["19", "/", "5"]]], " ", RowBox[List["(", RowBox[List["12", "+", RowBox[List["5", " ", "z"]]]], ")"]], " ", 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["625", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["39", "/", "5"]]]]]], "+", FractionBox[RowBox[List["3306", " ", RowBox[List["(", RowBox[List["1", "+", SqrtBox["5"]]], ")"]], " ", SuperscriptBox["z", RowBox[List["19", "/", "5"]]], " ", RowBox[List["(", RowBox[List["12", "+", RowBox[List["5", " ", "z"]]]], ")"]], " ", 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["625", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["39", "/", "5"]]]]]]]]]]]]

 MathML Form

 2 F 1 ( 2 , 3 ; - 14 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["14", "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] 6612 2 ( 5 + 5 ) ( 5 z + 12 ) tan - 1 ( 1 - ( 1 - 5 ) z 5 4 1 - z 5 , - 5 8 + 5 8 z 5 1 - z 5 ) z 19 / 5 625 ( 1 - z ) 39 / 5 + 6612 10 - 2 5 ( 5 z + 12 ) tan - 1 ( 1 - ( 1 + 5 ) z 5 4 1 - z 5 , - 5 8 - 5 8 z 5 1 - z 5 ) z 19 / 5 625 ( 1 - z ) 39 / 5 - 13224 ( 5 z + 12 ) log ( z 5 1 - z 5 + 1 ) z 19 / 5 625 ( 1 - z ) 39 / 5 - 3306 ( - 1 + 5 ) ( 5 z + 12 ) log ( z 2 / 5 ( 1 - z ) 2 / 5 - ( 1 - 5 ) z 5 2 1 - z 5 + 1 ) z 19 / 5 625 ( 1 - z ) 39 / 5 + 3306 ( 1 + 5 ) ( 5 z + 12 ) log ( z 2 / 5 ( 1 - z ) 2 / 5 - ( 1 + 5 ) z 5 2 1 - z 5 + 1 ) z 19 / 5 625 ( 1 - z ) 39 / 5 + 23940 z 5 + 750677 z 4 + 497500 z 3 - 113250 z 2 + 24000 z - 2625 2625 ( z - 1 ) 7 HypergeometricPFQ 2 3 -1 14 5 z 6612 2 5 5 1 2 1 2 5 z 12 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 19 5 625 1 -1 z 39 5 -1 6612 10 -1 2 5 1 2 1 2 5 z 12 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 19 5 625 1 -1 z 39 5 -1 -1 13224 5 z 12 z 1 5 1 -1 z 1 5 -1 1 z 19 5 625 1 -1 z 39 5 -1 -1 3306 -1 5 1 2 5 z 12 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 19 5 625 1 -1 z 39 5 -1 3306 1 5 1 2 5 z 12 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 19 5 625 1 -1 z 39 5 -1 23940 z 5 750677 z 4 497500 z 3 -1 113250 z 2 24000 z -2625 2625 z -1 7 -1 [/itex]

 Rule Form

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

 2007-05-02