Coth[I ArcTan[z]] == -(I/z)
Cell[BoxData[RowBox[List[RowBox[List["Coth", "[", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcTan", "[", "z", "]"]]]], "]"]], "\[Equal]", RowBox[List["-", FractionBox["\[ImaginaryI]", "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> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <msup> <mi> tan </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mo> - </mo> <mfrac> <mi> ⅈ </mi> <mi> z </mi> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <coth /> <apply> <times /> <imaginaryi /> <apply> <arctan /> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <power /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Coth", "[", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcTan", "[", "z_", "]"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox["\[ImaginaryI]", "z"]]]]]]]
2001-10-29
){kind=small}
