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http://functions.wolfram.com/01.23.27.0062.01
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Csch[z] + I Sech[z] == (I 2 Sqrt[2] Csch[2 z])/Csch[z - (Pi I)/4]
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Csch", "[", "z", "]"]], "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["Sech", "[", "z", "]"]]]]]], "\[Equal]", FractionBox[RowBox[List["\[ImaginaryI]", " ", "2", " ", SqrtBox["2"], " ", RowBox[List["Csch", "[", RowBox[List["2", " ", "z"]], "]"]]]], RowBox[List["Csch", "[", RowBox[List["z", "-", FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "4"]]], "]"]]]]]]]
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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> <mrow> <mi> csch </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <mi> sech </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ⩵ </mo> <mfrac> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mn> 2 </mn> <mo> ⁢ </mo> <msqrt> <mn> 2 </mn> </msqrt> <mo> ⁢ </mo> <mrow> <mi> csch </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mi> csch </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mfrac> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mi> ⅈ </mi> </mrow> <mn> 4 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <plus /> <apply> <csch /> <ci> z </ci> </apply> <apply> <times /> <imaginaryi /> <apply> <sech /> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <imaginaryi /> <cn type='integer'> 2 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <csch /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <csch /> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <pi /> <imaginaryi /> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["Csch", "[", "z_", "]"]], "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["Sech", "[", "z_", "]"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["\[ImaginaryI]", " ", "2", " ", SqrtBox["2"], " ", RowBox[List["Csch", "[", RowBox[List["2", " ", "z"]], "]"]]]], RowBox[List["Csch", "[", RowBox[List["z", "-", FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "4"]]], "]"]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
