Hyperbolic cotangent: General characteristics (formula 01.22.04.0001)

Coth

$Mathematica Notation$

Elementary Functions

Coth[z]

General characteristics

Domain and analyticity

http://functions.wolfram.com/01.22.04.0001.01

Input Form

DomainAndRange[Function[z, Coth[z]]] == Complexes \[LongRightArrow] Complexes

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["DomainAndRange", "[", RowBox[List["Function", "[", RowBox[List["z", ",", RowBox[List["Coth", "[", "z", "]"]]]], "]"]], "]"]], " ", "\[Equal]", RowBox[List["Complexes", "\[LongRightArrow]", "Complexes"]]]]]]

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> z </mi> <mo> ⟶ </mo> <mrow> <mi> coth </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ∷ </mo> <mrow> <mi> ℂ </mi> <mo> ⟶ </mo> <mi> ℂ </mi> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Proportion </ci> <apply> <ci> LongRightArrow </ci> <ci> z </ci> <apply> <coth /> <ci> z </ci> </apply> </apply> <apply> <ci> LongRightArrow </ci> <ci> ℂ </ci> <ci> ℂ </ci> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["DomainAndRange", "[", RowBox[List["Function", "[", RowBox[List["z_", ",", RowBox[List["Coth", "[", "z_", "]"]]]], "]"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["Complexes", "\[LongRightArrow]", "Complexes"]]]]]]

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

2001-10-29