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 Coth

 http://functions.wolfram.com/01.22.03.0037.01

 Input Form

 Coth[(3 Pi I)/7] == ((-2^(2/3)) (7 - 21 I Sqrt[3])^(1/3) + Sqrt[7] (I + Sqrt[3]) (7 - (I Sqrt[7])/2 - (3 Sqrt[21])/2)^(1/3) + 2 I Sqrt[7] (7 + (I Sqrt[7])/2 + (3 Sqrt[21])/2)^(1/3) + (14 - I Sqrt[7] - 3 Sqrt[21])^(2/3) (14 + I Sqrt[7] + 3 Sqrt[21])^(1/3) - (1/2) (14 - I Sqrt[7] - 3 Sqrt[21])^(1/3) (14 + I Sqrt[7] + 3 Sqrt[21])^ (2/3) - (1/2) I Sqrt[3] (14 - I Sqrt[7] - 3 Sqrt[21])^(1/3) (14 + I Sqrt[7] + 3 Sqrt[21])^(2/3))/ ((-I) 2^(2/3) 7^(5/6) (1 - 3 I Sqrt[3])^(1/3) + Sqrt[7] (I + Sqrt[3]) (7 - (I Sqrt[7])/2 - (3 Sqrt[21])/2)^(1/3) - (1/2) I (4 Sqrt[7] (7 + (I Sqrt[7])/2 + (3 Sqrt[21])/2)^(1/3) + (14 - 42 I Sqrt[3])^(1/3) (-2 I (14 - I Sqrt[7] - 3 Sqrt[21])^(1/3) + (-I + Sqrt[3]) (14 + I Sqrt[7] + 3 Sqrt[21])^(1/3))))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Coth", "[", FractionBox[RowBox[List["3", "\[Pi]", " ", "\[ImaginaryI]"]], "7"], "]"]], "\[Equal]", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox["2", RowBox[List["2", "/", "3"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["7", "-", RowBox[List["21", " ", "\[ImaginaryI]", " ", SqrtBox["3"]]]]], ")"]], RowBox[List["1", "/", "3"]]]]], "+", RowBox[List[SqrtBox["7"], " ", RowBox[List["(", RowBox[List["\[ImaginaryI]", "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["7", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SqrtBox["7"]]], "2"], "-", FractionBox[RowBox[List["3", " ", SqrtBox["21"]]], "2"]]], ")"]], RowBox[List["1", "/", "3"]]]]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", SqrtBox["7"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["7", "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", SqrtBox["7"]]], "2"], "+", FractionBox[RowBox[List["3", " ", SqrtBox["21"]]], "2"]]], ")"]], RowBox[List["1", "/", "3"]]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["14", "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox["7"]]], "-", RowBox[List["3", " ", SqrtBox["21"]]]]], ")"]], RowBox[List["2", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["14", "+", RowBox[List["\[ImaginaryI]", " ", SqrtBox["7"]]], "+", RowBox[List["3", " ", SqrtBox["21"]]]]], ")"]], RowBox[List["1", "/", "3"]]]]], "-", RowBox[List[FractionBox["1", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["14", "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox["7"]]], "-", RowBox[List["3", " ", SqrtBox["21"]]]]], ")"]], RowBox[List["1", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["14", "+", RowBox[List["\[ImaginaryI]", " ", SqrtBox["7"]]], "+", RowBox[List["3", " ", SqrtBox["21"]]]]], ")"]], RowBox[List["2", "/", "3"]]]]], "-", RowBox[List[FractionBox["1", "2"], " ", "\[ImaginaryI]", " ", SqrtBox["3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["14", "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox["7"]]], "-", RowBox[List["3", " ", SqrtBox["21"]]]]], ")"]], RowBox[List["1", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["14", "+", RowBox[List["\[ImaginaryI]", " ", SqrtBox["7"]]], "+", RowBox[List["3", " ", SqrtBox["21"]]]]], ")"]], RowBox[List["2", "/", "3"]]]]]]], ")"]], "/", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", SuperscriptBox["2", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox["7", RowBox[List["5", "/", "6"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", RowBox[List["3", " ", "\[ImaginaryI]", " ", SqrtBox["3"]]]]], ")"]], RowBox[List["1", "/", "3"]]]]], "+", RowBox[List[SqrtBox["7"], " ", RowBox[List["(", RowBox[List["\[ImaginaryI]", "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["7", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SqrtBox["7"]]], "2"], "-", FractionBox[RowBox[List["3", " ", SqrtBox["21"]]], "2"]]], ")"]], RowBox[List["1", "/", "3"]]]]], "-", RowBox[List[FractionBox["1", "2"], " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["4", " ", SqrtBox["7"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["7", "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", SqrtBox["7"]]], "2"], "+", FractionBox[RowBox[List["3", " ", SqrtBox["21"]]], "2"]]], ")"]], RowBox[List["1", "/", "3"]]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["14", "-", RowBox[List["42", " ", "\[ImaginaryI]", " ", SqrtBox["3"]]]]], ")"]], RowBox[List["1", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List["14", "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox["7"]]], "-", RowBox[List["3", " ", SqrtBox["21"]]]]], ")"]], RowBox[List["1", "/", "3"]]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["14", "+", RowBox[List["\[ImaginaryI]", " ", SqrtBox["7"]]], "+", RowBox[List["3", " ", SqrtBox["21"]]]]], ")"]], RowBox[List["1", "/", "3"]]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]]]]

 MathML Form

 coth ( 3 π 7 ) ( - 2 2 / 3 7 - 21 3 3 + 7 ( + 3 ) 7 - 7 2 - 3 21 2 3 + 2 7 7 + 7 2 + 3 21 2 3 + ( 14 - 7 - 3 21 ) 2 / 3 14 + 7 + 3 21 3 - 1 2 14 - 7 - 3 21 3 ( 14 + 7 + 3 21 ) 2 / 3 - 1 2 3 14 - 7 - 3 21 3 ( 14 + 7 + 3 21 ) 2 / 3 ) / ( - 2 2 / 3 7 5 / 6 1 - 3 3 3 + 7 ( + 3 ) 7 - 7 2 - 3 21 2 3 - 1 2 ( 4 7 7 + 7 2 + 3 21 2 3 + 14 - 42 3 3 ( - 2 14 - 7 - 3 21 3 + ( - + 3 ) 14 + 7 + 3 21 3 ) ) ) 3 7 -1 -1 2 2 3 7 -1 21 3 1 2 1 3 7 1 2 3 1 2 7 -1 7 1 2 2 -1 -1 3 21 1 2 2 -1 1 3 2 7 1 2 7 7 1 2 2 -1 3 21 1 2 2 -1 1 3 14 -1 7 1 2 -1 3 21 1 2 2 3 14 7 1 2 3 21 1 2 1 3 -1 1 2 14 -1 7 1 2 -1 3 21 1 2 1 3 14 7 1 2 3 21 1 2 2 3 -1 1 2 3 1 2 14 -1 7 1 2 -1 3 21 1 2 1 3 14 7 1 2 3 21 1 2 2 3 -1 2 2 3 7 5 6 1 -1 3 3 1 2 1 3 7 1 2 3 1 2 7 -1 7 1 2 2 -1 -1 3 21 1 2 2 -1 1 3 -1 1 2 4 7 1 2 7 7 1 2 2 -1 3 21 1 2 2 -1 1 3 14 -1 42 3 1 2 1 3 -2 14 -1 7 1 2 -1 3 21 1 2 1 3 -1 3 1 2 14 7 1 2 3 21 1 2 1 3 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Coth", "[", FractionBox[RowBox[List["3", " ", "\[Pi]", " ", "\[ImaginaryI]"]], "7"], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox["2", RowBox[List["2", "/", "3"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["7", "-", RowBox[List["21", " ", "\[ImaginaryI]", " ", SqrtBox["3"]]]]], ")"]], RowBox[List["1", "/", "3"]]]]], "+", RowBox[List[SqrtBox["7"], " ", RowBox[List["(", RowBox[List["\[ImaginaryI]", "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["7", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SqrtBox["7"]]], "2"], "-", FractionBox[RowBox[List["3", " ", SqrtBox["21"]]], "2"]]], ")"]], RowBox[List["1", "/", "3"]]]]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", SqrtBox["7"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["7", "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", SqrtBox["7"]]], "2"], "+", FractionBox[RowBox[List["3", " ", SqrtBox["21"]]], "2"]]], ")"]], RowBox[List["1", "/", "3"]]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["14", "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox["7"]]], "-", RowBox[List["3", " ", SqrtBox["21"]]]]], ")"]], RowBox[List["2", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["14", "+", RowBox[List["\[ImaginaryI]", " ", SqrtBox["7"]]], "+", RowBox[List["3", " ", SqrtBox["21"]]]]], ")"]], RowBox[List["1", "/", "3"]]]]], "-", RowBox[List[FractionBox["1", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["14", "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox["7"]]], "-", RowBox[List["3", " ", SqrtBox["21"]]]]], ")"]], RowBox[List["1", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["14", "+", RowBox[List["\[ImaginaryI]", " ", SqrtBox["7"]]], "+", RowBox[List["3", " ", SqrtBox["21"]]]]], ")"]], RowBox[List["2", "/", "3"]]]]], "-", RowBox[List[FractionBox["1", "2"], " ", "\[ImaginaryI]", " ", SqrtBox["3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["14", "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox["7"]]], "-", RowBox[List["3", " ", SqrtBox["21"]]]]], ")"]], RowBox[List["1", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["14", "+", RowBox[List["\[ImaginaryI]", " ", SqrtBox["7"]]], "+", RowBox[List["3", " ", SqrtBox["21"]]]]], ")"]], RowBox[List["2", "/", "3"]]]]]]], RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", SuperscriptBox["2", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox["7", RowBox[List["5", "/", "6"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", RowBox[List["3", " ", "\[ImaginaryI]", " ", SqrtBox["3"]]]]], ")"]], RowBox[List["1", "/", "3"]]]]], "+", RowBox[List[SqrtBox["7"], " ", RowBox[List["(", RowBox[List["\[ImaginaryI]", "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["7", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SqrtBox["7"]]], "2"], "-", FractionBox[RowBox[List["3", " ", SqrtBox["21"]]], "2"]]], ")"]], RowBox[List["1", "/", "3"]]]]], "-", RowBox[List[FractionBox["1", "2"], " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["4", " ", SqrtBox["7"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["7", "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", SqrtBox["7"]]], "2"], "+", FractionBox[RowBox[List["3", " ", SqrtBox["21"]]], "2"]]], ")"]], RowBox[List["1", "/", "3"]]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["14", "-", RowBox[List["42", " ", "\[ImaginaryI]", " ", SqrtBox["3"]]]]], ")"]], RowBox[List["1", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List["14", "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox["7"]]], "-", RowBox[List["3", " ", SqrtBox["21"]]]]], ")"]], RowBox[List["1", "/", "3"]]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["14", "+", RowBox[List["\[ImaginaryI]", " ", SqrtBox["7"]]], "+", RowBox[List["3", " ", SqrtBox["21"]]]]], ")"]], RowBox[List["1", "/", "3"]]]]]]], ")"]]]]]], ")"]]]]]]]]]]]

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

 2001-10-29

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