Coth[(Pi I)/7] == Root[1 + 21 #1^2 + 35 #1^4 + 7 #1^6 & , 5]

Cell[BoxData[RowBox[List[RowBox[List["Coth", "[", FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "7"], "]"]], "\[Equal]", RowBox[List["Root", "[", RowBox[List[RowBox[List[RowBox[List["1", "+", RowBox[List["21", " ", SuperscriptBox["#1", "2"]]], "+", RowBox[List["35", " ", SuperscriptBox["#1", "4"]]], "+", RowBox[List["7", " ", SuperscriptBox["#1", "6"]]]]], "&"]], ",", "5"]], "]"]]]]]]

<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> 7 </mn> </mfrac> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <msubsup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> ; </mo> <mrow> <mrow> <mn> 7 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 35 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 21 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 5 </mn> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msubsup> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <coth /> <apply> <times /> <pi /> <imaginaryi /> <apply> <power /> <cn type='integer'> 7 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <apply> <ci> CompoundExpression </ci> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 7 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 35 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 21 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> 5 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Coth", "[", FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "7"], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["Root", "[", RowBox[List[RowBox[List[RowBox[List["1", "+", RowBox[List["21", " ", SuperscriptBox["#1", "2"]]], "+", RowBox[List["35", " ", SuperscriptBox["#1", "4"]]], "+", RowBox[List["7", " ", SuperscriptBox["#1", "6"]]]]], "&"]], ",", "5"]], "]"]]]]]]

2001-10-29