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Csch




Mathematica Notation

Traditional Notation









Elementary Functions > Csch[z] > Representations through equivalent functions > With related functions > Involving sech





http://functions.wolfram.com/01.23.27.0063.01









  


  








Input Form





Csch[z] - I Sech[z] == -((I 2 Sqrt[2] Csch[2 z])/Csch[z + (Pi I)/4])








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Csch", "[", "z", "]"]], "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["Sech", "[", "z", "]"]]]]]], "\[Equal]", RowBox[List["-", 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"]]], "]"]]]]]]]]]








MathML Form







<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> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mi> sech </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mn> 2 </mn> </msqrt> <mo> &#8290; </mo> <mrow> <mi> csch </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mi> csch </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mfrac> <mrow> <mi> &#960; </mi> <mo> &#8290; </mo> <mi> &#8520; </mi> </mrow> <mn> 4 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <plus /> <apply> <csch /> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <sech /> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <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 /> <pi /> <imaginaryi /> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["Csch", "[", "z_", "]"]], "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["Sech", "[", "z_", "]"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List["-", 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"]]], "]"]]]]]]]]]


Date Added to functions.wolfram.com (modification date)





2001-10-29