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http://functions.wolfram.com/01.17.27.1140.01
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ArcCsc[Sqrt[2/(1 - Sqrt[1 + z^2])]] == -((I ArcSinh[z])/2) /;
Inequality[0, LessEqual, Arg[z], Less, Pi]
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcCsc", "[", SqrtBox[FractionBox["2", RowBox[List["1", "-", SqrtBox[RowBox[List["1", "+", SuperscriptBox["z", "2"]]]]]]]], "]"]], "\[Equal]", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSinh", "[", "z", "]"]]]], "2"]]]]], "/;", RowBox[List["0", "\[LessEqual]", RowBox[List["Arg", "[", "z", "]"]], "<", "\[Pi]"]]]]]]
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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> <msup> <mi> csc </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <msqrt> <mfrac> <mn> 2 </mn> <mrow> <mn> 1 </mn> <mo> - </mo> <msqrt> <mrow> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> </mrow> </mfrac> </msqrt> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <msup> <mi> sinh </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mn> 0 </mn> <mo> ≤ </mo> <mrow> <mi> arg </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> < </mo> <mi> π </mi> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <arccsc /> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <times /> <imaginaryi /> <apply> <arcsinh /> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <ci> Inequality </ci> <cn type='integer'> 0 </cn> <leq /> <apply> <arg /> <ci> z </ci> </apply> <lt /> <pi /> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCsc", "[", SqrtBox[FractionBox["2", RowBox[List["1", "-", SqrtBox[RowBox[List["1", "+", SuperscriptBox["z_", "2"]]]]]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSinh", "[", "z", "]"]]]], ")"]]]], "/;", RowBox[List["0", "\[LessEqual]", RowBox[List["Arg", "[", "z", "]"]], "<", "\[Pi]"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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