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ArcSech




Mathematica Notation

Traditional Notation









Elementary Functions > ArcSech[z] > Representations through equivalent functions > With related functions > Involving coth-1 > Involving sech-1(z-1/z+1) > Involving sech-1(z-1/z+1) and coth-1(1/z1/2)





http://functions.wolfram.com/01.30.27.2317.01









  


  








Input Form





ArcSech[(z - 1)/(z + 1)] == (-Pi) I + 2 ArcCoth[Sqrt[1/z]] /; Im[z] > 0








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcSech", "[", FractionBox[RowBox[List["z", "-", "1"]], RowBox[List["z", "+", "1"]]], "]"]], "\[Equal]", RowBox[List[RowBox[List[RowBox[List["-", "\[Pi]"]], " ", "\[ImaginaryI]"]], "+", RowBox[List["2", " ", RowBox[List["ArcCoth", "[", SqrtBox[FractionBox["1", "z"]], "]"]]]]]]]], "/;", RowBox[List[RowBox[List["Im", "[", "z", "]"]], ">", "0"]]]]]]








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> <msup> <mi> sech </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mfrac> <mrow> <mi> z </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mfrac> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mi> &#960; </mi> </mrow> <mo> &#8290; </mo> <mi> &#8520; </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <msup> <mi> coth </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <msqrt> <mfrac> <mn> 1 </mn> <mi> z </mi> </mfrac> </msqrt> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> Im </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &gt; </mo> <mn> 0 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <arcsech /> <apply> <times /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <pi /> </apply> <imaginaryi /> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <arccoth /> <apply> <power /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <gt /> <apply> <imaginary /> <ci> z </ci> </apply> <cn type='integer'> 0 </cn> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcSech", "[", FractionBox[RowBox[List["z_", "-", "1"]], RowBox[List["z_", "+", "1"]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List[RowBox[List["-", "\[Pi]"]], " ", "\[ImaginaryI]"]], "+", RowBox[List["2", " ", RowBox[List["ArcCoth", "[", SqrtBox[FractionBox["1", "z"]], "]"]]]]]], "/;", RowBox[List[RowBox[List["Im", "[", "z", "]"]], ">", "0"]]]]]]]]


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





2003-08-21