Coth[(Pi I)/17] == (-I) Sqrt[(15 + Sqrt[17] + Sqrt[34 - 2 Sqrt[17]] + Sqrt[2 (34 + 6 Sqrt[17] - Sqrt[34 - 2 Sqrt[17]] + Sqrt[34 (17 - Sqrt[17])] - 8 Sqrt[2 (17 + Sqrt[17])])])/ (16 - 2 Sqrt[2 (15 + Sqrt[17] - Sqrt[34 - 2 Sqrt[17]] + Sqrt[2 (34 + 6 Sqrt[17] + Sqrt[34 - 2 Sqrt[17]] - Sqrt[34 (17 - Sqrt[17])] + 8 Sqrt[2 (17 + Sqrt[17])])])])]

Cell[BoxData[RowBox[List[RowBox[List["Coth", "[", FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "17"], "]"]], "\[Equal]", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", RowBox[List["\[Sqrt]", RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["15", "+", SqrtBox["17"], "+", SqrtBox[RowBox[List["34", "-", RowBox[List["2", " ", SqrtBox["17"]]]]]], "+", RowBox[List["\[Sqrt]", RowBox[List["(", RowBox[List["2", " ", RowBox[List["(", RowBox[List["34", "+", RowBox[List["6", " ", SqrtBox["17"]]], "-", SqrtBox[RowBox[List["34", "-", RowBox[List["2", " ", SqrtBox["17"]]]]]], "+", SqrtBox[RowBox[List["34", " ", RowBox[List["(", RowBox[List["17", "-", SqrtBox["17"]]], ")"]]]]], "-", RowBox[List["8", " ", SqrtBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List["17", "+", SqrtBox["17"]]], ")"]]]]]]]]], ")"]]]], ")"]]]]]], ")"]], "/", RowBox[List["(", RowBox[List["16", "-", RowBox[List["2", " ", RowBox[List["\[Sqrt]", RowBox[List["(", RowBox[List["2", " ", RowBox[List["(", RowBox[List["15", "+", SqrtBox["17"], "-", SqrtBox[RowBox[List["34", "-", RowBox[List["2", " ", SqrtBox["17"]]]]]], "+", RowBox[List["\[Sqrt]", RowBox[List["(", RowBox[List["2", " ", RowBox[List["(", RowBox[List["34", "+", RowBox[List["6", " ", SqrtBox["17"]]], "+", SqrtBox[RowBox[List["34", "-", RowBox[List["2", " ", SqrtBox["17"]]]]]], "-", SqrtBox[RowBox[List["34", " ", RowBox[List["(", RowBox[List["17", "-", SqrtBox["17"]]], ")"]]]]], "+", RowBox[List["8", " ", SqrtBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List["17", "+", SqrtBox["17"]]], ")"]]]]]]]]], ")"]]]], ")"]]]]]], ")"]]]], ")"]]]]]]]], ")"]]]], ")"]]]]]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mi> coth </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mrow> <mi> &#960; </mi> <mo> &#8290; </mo> <mi> &#8520; </mi> </mrow> <mn> 17 </mn> </mfrac> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mo> - </mo> <mi> &#8520; </mi> </mrow> <mo> &#8290; </mo> <mrow> <mo> &#8730; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> &#8730; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msqrt> <mrow> <mn> 34 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 17 </mn> <mo> - </mo> <msqrt> <mn> 17 </mn> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> </msqrt> <mo> + </mo> <mrow> <mn> 6 </mn> <mo> &#8290; </mo> <msqrt> <mn> 17 </mn> </msqrt> </mrow> <mo> - </mo> <mrow> <mn> 8 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 17 </mn> <mo> + </mo> <msqrt> <mn> 17 </mn> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> </msqrt> </mrow> <mo> - </mo> <msqrt> <mrow> <mn> 34 </mn> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mn> 17 </mn> </msqrt> </mrow> </mrow> </msqrt> <mo> + </mo> <mn> 34 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <msqrt> <mn> 17 </mn> </msqrt> <mo> + </mo> <msqrt> <mrow> <mn> 34 </mn> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mn> 17 </mn> </msqrt> </mrow> </mrow> </msqrt> <mo> + </mo> <mn> 15 </mn> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mn> 16 </mn> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mo> &#8730; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> &#8730; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <msqrt> <mrow> <mn> 34 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 17 </mn> <mo> - </mo> <msqrt> <mn> 17 </mn> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> </msqrt> </mrow> <mo> + </mo> <mrow> <mn> 6 </mn> <mo> &#8290; </mo> <msqrt> <mn> 17 </mn> </msqrt> </mrow> <mo> + </mo> <mrow> <mn> 8 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 17 </mn> <mo> + </mo> <msqrt> <mn> 17 </mn> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> </msqrt> </mrow> <mo> + </mo> <msqrt> <mrow> <mn> 34 </mn> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mn> 17 </mn> </msqrt> </mrow> </mrow> </msqrt> <mo> + </mo> <mn> 34 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <msqrt> <mn> 17 </mn> </msqrt> <mo> - </mo> <msqrt> <mrow> <mn> 34 </mn> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mn> 17 </mn> </msqrt> </mrow> </mrow> </msqrt> <mo> + </mo> <mn> 15 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <coth /> <apply> <times /> <pi /> <imaginaryi /> <apply> <power /> <cn type='integer'> 17 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <apply> <root /> <apply> <times /> <apply> <plus /> <apply> <root /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <power /> <apply> <times /> <cn type='integer'> 34 </cn> <apply> <plus /> <cn type='integer'> 17 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <cn type='integer'> 17 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <times /> <cn type='integer'> 6 </cn> <apply> <power /> <cn type='integer'> 17 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 8 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <cn type='integer'> 17 </cn> <apply> <power /> <cn type='integer'> 17 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 34 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <cn type='integer'> 17 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 34 </cn> </apply> </apply> </apply> <apply> <power /> <cn type='integer'> 17 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 34 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <cn type='integer'> 17 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 15 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 16 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <root /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <root /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 34 </cn> <apply> <plus /> <cn type='integer'> 17 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <cn type='integer'> 17 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 6 </cn> <apply> <power /> <cn type='integer'> 17 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 8 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <cn type='integer'> 17 </cn> <apply> <power /> <cn type='integer'> 17 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 34 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <cn type='integer'> 17 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 34 </cn> </apply> </apply> </apply> <apply> <power /> <cn type='integer'> 17 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 34 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <cn type='integer'> 17 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 15 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Coth", "[", FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "17"], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", SqrtBox[FractionBox[RowBox[List["15", "+", SqrtBox["17"], "+", SqrtBox[RowBox[List["34", "-", RowBox[List["2", " ", SqrtBox["17"]]]]]], "+", SqrtBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List["34", "+", RowBox[List["6", " ", SqrtBox["17"]]], "-", SqrtBox[RowBox[List["34", "-", RowBox[List["2", " ", SqrtBox["17"]]]]]], "+", SqrtBox[RowBox[List["34", " ", RowBox[List["(", RowBox[List["17", "-", SqrtBox["17"]]], ")"]]]]], "-", RowBox[List["8", " ", SqrtBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List["17", "+", SqrtBox["17"]]], ")"]]]]]]]]], ")"]]]]]]], RowBox[List["16", "-", RowBox[List["2", " ", SqrtBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List["15", "+", SqrtBox["17"], "-", SqrtBox[RowBox[List["34", "-", RowBox[List["2", " ", SqrtBox["17"]]]]]], "+", SqrtBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List["34", "+", RowBox[List["6", " ", SqrtBox["17"]]], "+", SqrtBox[RowBox[List["34", "-", RowBox[List["2", " ", SqrtBox["17"]]]]]], "-", SqrtBox[RowBox[List["34", " ", RowBox[List["(", RowBox[List["17", "-", SqrtBox["17"]]], ")"]]]]], "+", RowBox[List["8", " ", SqrtBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List["17", "+", SqrtBox["17"]]], ")"]]]]]]]]], ")"]]]]]]], ")"]]]]]]]]]]]]]]]]]

2001-10-29