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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[1, 3, -(11/4), z] == (1/19712) ((8 (2464 - 17472 z + 59232 z^2 - 167424 z^3 - 49665 z^4 + 4620 z^5))/(-1 + z)^6 + (1009470 Sqrt[2] z^(15/4) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))])/(1 - z)^(27/4) + (1009470 Sqrt[2] z^(15/4) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))])/(1 - z)^(27/4) + (504735 Sqrt[2] z^(15/4) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]])/(1 - z)^(27/4) - (504735 Sqrt[2] z^(15/4) Log[1 + (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]])/(1 - z)^(27/4))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List["1", ",", "3", ",", RowBox[List["-", FractionBox["11", "4"]]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "19712"], RowBox[List["(", RowBox[List[FractionBox[RowBox[List["8", " ", RowBox[List["(", RowBox[List["2464", "-", RowBox[List["17472", " ", "z"]], "+", RowBox[List["59232", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["167424", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["49665", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["4620", " ", SuperscriptBox["z", "5"]]]]], ")"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "6"]], "+", FractionBox[RowBox[List["1009470", " ", SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["15", "/", "4"]]], " ", RowBox[List["ArcTan", "[", RowBox[List[RowBox[List["1", "-", FractionBox[SuperscriptBox["z", RowBox[List["1", "/", "4"]]], RowBox[List[SqrtBox["2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox["z", RowBox[List["1", "/", "4"]]], RowBox[List[SqrtBox["2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["27", "/", "4"]]]], "+", FractionBox[RowBox[List["1009470", " ", SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["15", "/", "4"]]], " ", RowBox[List["ArcTan", "[", RowBox[List[RowBox[List["1", "+", FractionBox[SuperscriptBox["z", RowBox[List["1", "/", "4"]]], RowBox[List[SqrtBox["2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox["z", RowBox[List["1", "/", "4"]]], RowBox[List[SqrtBox["2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["27", "/", "4"]]]], "+", FractionBox[RowBox[List["504735", " ", SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["15", "/", "4"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", FractionBox[RowBox[List[SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]], "+", FractionBox[SqrtBox["z"], SqrtBox[RowBox[List["1", "-", "z"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["27", "/", "4"]]]], "-", FractionBox[RowBox[List["504735", " ", SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["15", "/", "4"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", FractionBox[RowBox[List[SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]], "+", FractionBox[SqrtBox["z"], SqrtBox[RowBox[List["1", "-", "z"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["27", "/", "4"]]]]]], ")"]]]]]]]]

 MathML Form

 2 F 1 ( 1 , 3 ; - 11 4 ; 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["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["11", "4"]]], 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] 1 19712 ( 1009470 2 tan - 1 ( 1 - z 4 2 1 - z 4 , - z 4 2 1 - z 4 ) z 15 / 4 ( 1 - z ) 27 / 4 + 1009470 2 tan - 1 ( z 4 2 1 - z 4 + 1 , - z 4 2 1 - z 4 ) z 15 / 4 ( 1 - z ) 27 / 4 + 504735 2 log ( z 1 - z - 2 z 4 1 - z 4 + 1 ) z 15 / 4 ( 1 - z ) 27 / 4 - 504735 2 log ( z 1 - z + 2 z 4 1 - z 4 + 1 ) z 15 / 4 ( 1 - z ) 27 / 4 + 8 ( 4620 z 5 - 49665 z 4 - 167424 z 3 + 59232 z 2 - 17472 z + 2464 ) ( z - 1 ) 6 ) HypergeometricPFQ 1 3 -1 11 4 z 1 19712 1009470 2 1 2 1 -1 z 1 4 2 1 2 1 -1 z 1 4 -1 -1 z 1 4 2 1 2 1 -1 z 1 4 -1 z 15 4 1 -1 z 27 4 -1 1009470 2 1 2 z 1 4 2 1 2 1 -1 z 1 4 -1 1 -1 z 1 4 2 1 2 1 -1 z 1 4 -1 z 15 4 1 -1 z 27 4 -1 504735 2 1 2 z 1 2 1 -1 z 1 2 -1 -1 2 1 2 z 1 4 1 -1 z 1 4 -1 1 z 15 4 1 -1 z 27 4 -1 -1 504735 2 1 2 z 1 2 1 -1 z 1 2 -1 2 1 2 z 1 4 1 -1 z 1 4 -1 1 z 15 4 1 -1 z 27 4 -1 8 4620 z 5 -1 49665 z 4 -1 167424 z 3 59232 z 2 -1 17472 z 2464 z -1 6 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List["1", ",", "3", ",", RowBox[List["-", FractionBox["11", "4"]]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[FractionBox[RowBox[List["8", " ", RowBox[List["(", RowBox[List["2464", "-", RowBox[List["17472", " ", "z"]], "+", RowBox[List["59232", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["167424", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["49665", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["4620", " ", SuperscriptBox["z", "5"]]]]], ")"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "6"]], "+", FractionBox[RowBox[List["1009470", " ", SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["15", "/", "4"]]], " ", RowBox[List["ArcTan", "[", RowBox[List[RowBox[List["1", "-", FractionBox[SuperscriptBox["z", RowBox[List["1", "/", "4"]]], RowBox[List[SqrtBox["2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox["z", RowBox[List["1", "/", "4"]]], RowBox[List[SqrtBox["2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["27", "/", "4"]]]], "+", FractionBox[RowBox[List["1009470", " ", SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["15", "/", "4"]]], " ", RowBox[List["ArcTan", "[", RowBox[List[RowBox[List["1", "+", FractionBox[SuperscriptBox["z", RowBox[List["1", "/", "4"]]], RowBox[List[SqrtBox["2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox["z", RowBox[List["1", "/", "4"]]], RowBox[List[SqrtBox["2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["27", "/", "4"]]]], "+", FractionBox[RowBox[List["504735", " ", SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["15", "/", "4"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", FractionBox[RowBox[List[SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]], "+", FractionBox[SqrtBox["z"], SqrtBox[RowBox[List["1", "-", "z"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["27", "/", "4"]]]], "-", FractionBox[RowBox[List["504735", " ", SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["15", "/", "4"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", FractionBox[RowBox[List[SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]], "+", FractionBox[SqrtBox["z"], SqrtBox[RowBox[List["1", "-", "z"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["27", "/", "4"]]]]]], "19712"]]]]]

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

 2007-05-02