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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.b0uf.01

 Input Form

 Hypergeometric2F1[2, 2, -(19/5), z] == -((9975 - 80325 z + 299850 z^2 - 737750 z^3 + 1811625 z^4 + 1057109 z^5)/ (9975 (-1 + z)^7)) - (348 Sqrt[2 (5 + Sqrt[5])] z^(24/5) (29 + 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))])/ (125 (1 - z)^(39/5)) - (348 Sqrt[10 - 2 Sqrt[5]] z^(24/5) (29 + 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))])/ (125 (1 - z)^(39/5)) + (696 z^(24/5) (29 + 5 z) Log[1 + z^(1/5)/(1 - z)^(1/5)])/(125 (1 - z)^(39/5)) + (174 (-1 + Sqrt[5]) z^(24/5) (29 + 5 z) Log[1 - ((1 - Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(125 (1 - z)^(39/5)) - (174 (1 + Sqrt[5]) z^(24/5) (29 + 5 z) Log[1 - ((1 + Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(125 (1 - z)^(39/5))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List["2", ",", "2", ",", RowBox[List["-", FractionBox["19", "5"]]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["9975", "-", RowBox[List["80325", " ", "z"]], "+", RowBox[List["299850", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["737750", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["1811625", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["1057109", " ", SuperscriptBox["z", "5"]]]]], RowBox[List["9975", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "7"]]]]]], "-", FractionBox[RowBox[List["348", " ", SqrtBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List["5", "+", SqrtBox["5"]]], ")"]]]]], " ", SuperscriptBox["z", RowBox[List["24", "/", "5"]]], " ", RowBox[List["(", RowBox[List["29", "+", 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["125", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["39", "/", "5"]]]]]], "-", FractionBox[RowBox[List["348", " ", SqrtBox[RowBox[List["10", "-", RowBox[List["2", " ", SqrtBox["5"]]]]]], " ", SuperscriptBox["z", RowBox[List["24", "/", "5"]]], " ", RowBox[List["(", RowBox[List["29", "+", 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["125", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["39", "/", "5"]]]]]], "+", FractionBox[RowBox[List["696", " ", SuperscriptBox["z", RowBox[List["24", "/", "5"]]], " ", RowBox[List["(", RowBox[List["29", "+", 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["125", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["39", "/", "5"]]]]]], "+", FractionBox[RowBox[List["174", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox["5"]]], ")"]], " ", SuperscriptBox["z", RowBox[List["24", "/", "5"]]], " ", RowBox[List["(", RowBox[List["29", "+", 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["125", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["39", "/", "5"]]]]]], "-", FractionBox[RowBox[List["174", " ", RowBox[List["(", RowBox[List["1", "+", SqrtBox["5"]]], ")"]], " ", SuperscriptBox["z", RowBox[List["24", "/", "5"]]], " ", RowBox[List["(", RowBox[List["29", "+", 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["125", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["39", "/", "5"]]]]]]]]]]]]

 MathML Form

 2 F 1 ( 2 , 2 ; - 19 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["2", 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["19", "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] - 348 2 ( 5 + 5 ) ( 5 z + 29 ) tan - 1 ( 1 - ( 1 - 5 ) z 5 4 1 - z 5 , - 5 8 + 5 8 z 5 1 - z 5 ) z 24 / 5 125 ( 1 - z ) 39 / 5 - 348 10 - 2 5 ( 5 z + 29 ) tan - 1 ( 1 - ( 1 + 5 ) z 5 4 1 - z 5 , - 5 8 - 5 8 z 5 1 - z 5 ) z 24 / 5 125 ( 1 - z ) 39 / 5 + 696 ( 5 z + 29 ) log ( z 5 1 - z 5 + 1 ) z 24 / 5 125 ( 1 - z ) 39 / 5 + 174 ( - 1 + 5 ) ( 5 z + 29 ) log ( z 2 / 5 ( 1 - z ) 2 / 5 - ( 1 - 5 ) z 5 2 1 - z 5 + 1 ) z 24 / 5 125 ( 1 - z ) 39 / 5 - 174 ( 1 + 5 ) ( 5 z + 29 ) log ( z 2 / 5 ( 1 - z ) 2 / 5 - ( 1 + 5 ) z 5 2 1 - z 5 + 1 ) z 24 / 5 125 ( 1 - z ) 39 / 5 - 1057109 z 5 + 1811625 z 4 - 737750 z 3 + 299850 z 2 - 80325 z + 9975 9975 ( z - 1 ) 7 HypergeometricPFQ 2 2 -1 19 5 z -1 348 2 5 5 1 2 1 2 5 z 29 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 24 5 125 1 -1 z 39 5 -1 -1 348 10 -1 2 5 1 2 1 2 5 z 29 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 24 5 125 1 -1 z 39 5 -1 696 5 z 29 z 1 5 1 -1 z 1 5 -1 1 z 24 5 125 1 -1 z 39 5 -1 174 -1 5 1 2 5 z 29 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 24 5 125 1 -1 z 39 5 -1 -1 174 1 5 1 2 5 z 29 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 24 5 125 1 -1 z 39 5 -1 -1 1057109 z 5 1811625 z 4 -1 737750 z 3 299850 z 2 -1 80325 z 9975 9975 z -1 7 -1 [/itex]

 Rule Form

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

 2007-05-02