Hyperbolic cotangent: Specific values (formula 01.22.03.0029)

Coth

$Mathematica Notation$

Elementary Functions

Specific values

Values at fixed points

http://functions.wolfram.com/01.22.03.0029.01

Input Form

Coth[(Pi I)/3] == -(I/Sqrt[3])

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["Coth", "[", FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "3"], "]"]], "\[Equal]", RowBox[List["-", FractionBox["\[ImaginaryI]", SqrtBox["3"]]]]]]]]

MathML Form

<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> ⁡ </mo> <mo> ( </mo> <mfrac> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mi> ⅈ </mi> </mrow> <mn> 3 </mn> </mfrac> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mo> - </mo> <mfrac> <mi> ⅈ </mi> <msqrt> <mn> 3 </mn> </msqrt> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <coth /> <apply> <times /> <pi /> <imaginaryi /> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <power /> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Coth", "[", FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "3"], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox["\[ImaginaryI]", SqrtBox["3"]]]]]]]]

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

2001-10-29