ArcCoth[1/z] == ArcTanh[z]
Cell[BoxData[RowBox[List[RowBox[List["ArcCoth", "[", FractionBox["1", "z"], "]"]], "\[Equal]", RowBox[List["ArcTanh", "[", "z", "]"]]]]]]
<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msup> <mi> coth </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mfrac> <mn> 1 </mn> <mi> z </mi> </mfrac> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <msup> <mi> tanh </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <arccoth /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <arctanh /> <ci> z </ci> </apply> </apply> </annotation-xml> </semantics> </math>
Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCoth", "[", FractionBox["1", "z_"], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["ArcTanh", "[", "z", "]"]]]]]]
2003-09-04
){kind=small}
