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http://functions.wolfram.com/01.28.27.0821.01
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ArcCoth[1/z] == (-I) ArcTan[I z]
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Cell[BoxData[RowBox[List[RowBox[List["ArcCoth", "[", FractionBox["1", "z"], "]"]], "\[Equal]", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", RowBox[List["ArcTan", "[", RowBox[List["\[ImaginaryI]", " ", "z"]], "]"]]]]]]]]
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<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> <mrow> <mo> - </mo> <mi> ⅈ </mi> </mrow> <mo> ⁢ </mo> <mrow> <msup> <mi> tan </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </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> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <apply> <arctan /> <apply> <times /> <imaginaryi /> <ci> z </ci> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCoth", "[", FractionBox["1", "z_"], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", RowBox[List["ArcTan", "[", RowBox[List["\[ImaginaryI]", " ", "z"]], "]"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
