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ArcCsch




Mathematica Notation

Traditional Notation









Elementary Functions > ArcCsch[z] > Representations through equivalent functions > With related functions > Involving cos-1 > Involving csch-1(z) > Involving csch-1(z) and cos-1((-z2-1)1/2/(-z2)1/2)





http://functions.wolfram.com/01.29.27.0264.01









  


  








Input Form





ArcCsch[z] == (-z) Sqrt[-z^(-2)] ArcCos[Sqrt[-z^2 - 1]/Sqrt[-z^2]]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["ArcCsch", "[", "z", "]"]], "\[Equal]", RowBox[List[RowBox[List["-", "z"]], SqrtBox[RowBox[List["-", SuperscriptBox["z", RowBox[List["-", "2"]]]]]], RowBox[List["ArcCos", "[", FractionBox[SqrtBox[RowBox[List[RowBox[List["-", SuperscriptBox["z", "2"]]], "-", "1"]]], SqrtBox[RowBox[List["-", SuperscriptBox["z", "2"]]]]], "]"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msup> <mi> csch </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> &#8290; </mo> <msqrt> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mfrac> </mrow> </msqrt> <mo> &#8290; </mo> <mrow> <msup> <mi> cos </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mfrac> <msqrt> <mrow> <mrow> <mo> - </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msqrt> <msqrt> <mrow> <mo> - </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> </mfrac> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <arccsch /> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <arccos /> <apply> <times /> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCsch", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", "z"]], " ", SqrtBox[RowBox[List["-", FractionBox["1", SuperscriptBox["z", "2"]]]]], " ", RowBox[List["ArcCos", "[", FractionBox[SqrtBox[RowBox[List[RowBox[List["-", SuperscriptBox["z", "2"]]], "-", "1"]]], SqrtBox[RowBox[List["-", SuperscriptBox["z", "2"]]]]], "]"]]]]]]]]


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





2003-08-21