Coth[ArcSinh[z]] == Sqrt[1 + z^2]/z
Cell[BoxData[RowBox[List[RowBox[List["Coth", "[", RowBox[List["ArcSinh", "[", "z", "]"]], "]"]], "\[Equal]", FractionBox[SqrtBox[RowBox[List["1", "+", SuperscriptBox["z", "2"]]]], "z"]]]]]
<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> <mrow> <msup> <mi> sinh </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mfrac> <msqrt> <mrow> <mn> 1 </mn> <mo> + </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> <mi> z </mi> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <coth /> <apply> <arcsinh /> <ci> z </ci> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Coth", "[", RowBox[List["ArcSinh", "[", "z_", "]"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[SqrtBox[RowBox[List["1", "+", SuperscriptBox["z", "2"]]]], "z"]]]]]
2001-10-29
){kind=small}
