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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.al26.01

 Input Form

 Hypergeometric2F1[2, 6, 19/4, z] == (1/(262144 (-1 + z)^3 z^(15/4))) (11 (8 z^(3/4) (-385 + 480 z + 240 z^2 - 2816 z^3 + 1536 z^4) + (210 Sqrt[2] (-11 + 20 z) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))])/(1 - z)^(1/4) + (210 Sqrt[2] (-11 + 20 z) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))])/(1 - z)^(1/4) - (105 Sqrt[2] (-11 + 20 z) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]])/(1 - z)^(1/4) + (105 Sqrt[2] (-11 + 20 z) Log[1 + (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]])/(1 - z)^(1/4)))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List["2", ",", "6", ",", FractionBox["19", "4"], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["262144", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "3"], " ", SuperscriptBox["z", RowBox[List["15", "/", "4"]]]]]], RowBox[List["(", RowBox[List["11", " ", RowBox[List["(", RowBox[List[RowBox[List["8", " ", SuperscriptBox["z", RowBox[List["3", "/", "4"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "385"]], "+", RowBox[List["480", " ", "z"]], "+", RowBox[List["240", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["2816", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["1536", " ", SuperscriptBox["z", "4"]]]]], ")"]]]], "+", FractionBox[RowBox[List["210", " ", SqrtBox["2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "11"]], "+", RowBox[List["20", " ", "z"]]]], ")"]], " ", 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["1", "/", "4"]]]], "+", FractionBox[RowBox[List["210", " ", SqrtBox["2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "11"]], "+", RowBox[List["20", " ", "z"]]]], ")"]], " ", 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["1", "/", "4"]]]], "-", FractionBox[RowBox[List["105", " ", SqrtBox["2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "11"]], "+", RowBox[List["20", " ", "z"]]]], ")"]], " ", 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["1", "/", "4"]]]], "+", FractionBox[RowBox[List["105", " ", SqrtBox["2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "11"]], "+", RowBox[List["20", " ", "z"]]]], ")"]], " ", 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["1", "/", "4"]]]]]], ")"]]]], ")"]]]]]]]]

 MathML Form

 2 F 1 ( 2 , 6 ; 19 4 ; 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["6", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["19", "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 262144 ( z - 1 ) 3 z 15 / 4 ( 11 ( 8 z 3 / 4 ( 1536 z 4 - 2816 z 3 + 240 z 2 + 480 z - 385 ) + 210 2 ( 20 z - 11 ) tan - 1 ( 1 - z 4 2 1 - z 4 , - z 4 2 1 - z 4 ) 1 - z 4 + 210 2 ( 20 z - 11 ) tan - 1 ( z 4 2 1 - z 4 + 1 , - z 4 2 1 - z 4 ) 1 - z 4 - 105 2 ( 20 z - 11 ) log ( z 1 - z - 2 z 4 1 - z 4 + 1 ) 1 - z 4 + 105 2 ( 20 z - 11 ) log ( z 1 - z + 2 z 4 1 - z 4 + 1 ) 1 - z 4 ) ) HypergeometricPFQ 2 6 19 4 z 1 262144 z -1 3 z 15 4 -1 11 8 z 3 4 1536 z 4 -1 2816 z 3 240 z 2 480 z -385 210 2 1 2 20 z -11 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 1 -1 z 1 4 -1 210 2 1 2 20 z -11 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 1 -1 z 1 4 -1 -1 105 2 1 2 20 z -11 z 1 2 1 -1 z 1 2 -1 -1 2 1 2 z 1 4 1 -1 z 1 4 -1 1 1 -1 z 1 4 -1 105 2 1 2 20 z -11 z 1 2 1 -1 z 1 2 -1 2 1 2 z 1 4 1 -1 z 1 4 -1 1 1 -1 z 1 4 -1 [/itex]

 Rule Form

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

 2007-05-02