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ArcTanh




Mathematica Notation

Traditional Notation









Elementary Functions > ArcTanh[z] > Representations through equivalent functions > With inverse function > Involving tanh-1(coth(z))





http://functions.wolfram.com/01.27.27.3490.01









  


  








Input Form





ArcTanh[Coth[z]] == ArcCoth[Tanh[z]] /; !Element[(I z)/Pi, Integers]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcTanh", "[", RowBox[List["Coth", "[", "z", "]"]], "]"]], "\[Equal]", RowBox[List["ArcCoth", "[", RowBox[List["Tanh", "[", "z", "]"]], "]"]]]], "/;", RowBox[List["Not", "[", RowBox[List[FractionBox[RowBox[List["\[ImaginaryI]", " ", "z"]], "\[Pi]"], "\[Element]", "Integers"]], "]"]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <msup> <mi> tanh </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mi> coth </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mo> &#63449; </mo> <mrow> <msup> <mi> coth </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mi> tanh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mfrac> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mi> &#960; </mi> </mfrac> <mo> &#8713; </mo> <semantics> <mi> &#8484; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalZ]&quot;, Function[List[], Integers]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <arctanh /> <apply> <coth /> <ci> z </ci> </apply> </apply> <apply> <arccoth /> <apply> <tanh /> <ci> z </ci> </apply> </apply> </apply> <apply> <notin /> <apply> <times /> <imaginaryi /> <ci> z </ci> <apply> <power /> <pi /> <cn type='integer'> -1 </cn> </apply> </apply> <integers /> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcTanh", "[", RowBox[List["Coth", "[", "z_", "]"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["ArcCoth", "[", RowBox[List["Tanh", "[", "z", "]"]], "]"]], "/;", RowBox[List["!", RowBox[List[FractionBox[RowBox[List["\[ImaginaryI]", " ", "z"]], "\[Pi]"], "\[Element]", "Integers"]]]]]]]]]]


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





2007-05-02