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ArcSech




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.30.27.0973.01









  


  








Input Form





ArcSech[Sqrt[-1 - z]/Sqrt[-z]] == I ArcCot[Sqrt[z]] /; Im[z] >= 0








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcSech", "[", FractionBox[SqrtBox[RowBox[List[RowBox[List["-", "1"]], "-", "z"]]], SqrtBox[RowBox[List["-", "z"]]]], "]"]], "\[Equal]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcCot", "[", SqrtBox["z"], "]"]]]]]], " ", "/;", RowBox[List[RowBox[List["Im", "[", "z", "]"]], "\[GreaterEqual]", "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> <msqrt> <mrow> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> <msqrt> <mrow> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> </mfrac> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <msup> <mi> cot </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> Im </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8805; </mo> <mn> 0 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <arcsech /> <apply> <times /> <apply> <power /> <apply> <plus /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <imaginaryi /> <apply> <arccot /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> <apply> <geq /> <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[SqrtBox[RowBox[List[RowBox[List["-", "1"]], "-", "z_"]]], SqrtBox[RowBox[List["-", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcCot", "[", SqrtBox["z"], "]"]]]], "/;", RowBox[List[RowBox[List["Im", "[", "z", "]"]], "\[GreaterEqual]", "0"]]]]]]]]


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





2003-08-21