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http://functions.wolfram.com/01.21.27.0012.01
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Tanh[z] == (-I) (Cos[Pi/2 - I z]/Cos[I z])
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Cell[BoxData[RowBox[List[RowBox[List["Tanh", "[", "z", "]"]], "\[Equal]", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], FractionBox[RowBox[List["Cos", "[", RowBox[List[FractionBox["\[Pi]", "2"], "-", RowBox[List["\[ImaginaryI]", " ", "z"]]]], "]"]], RowBox[List["Cos", "[", 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> <mi> tanh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mfrac> <mi> π </mi> <mn> 2 </mn> </mfrac> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <tanh /> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <cos /> <apply> <plus /> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <cos /> <apply> <times /> <imaginaryi /> <ci> z </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Tanh", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["Cos", "[", RowBox[List[FractionBox["\[Pi]", "2"], "-", RowBox[List["\[ImaginaryI]", " ", "z"]]]], "]"]]]], RowBox[List["Cos", "[", RowBox[List["\[ImaginaryI]", " ", "z"]], "]"]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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