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http://functions.wolfram.com/01.18.27.0703.01
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ArcSec[(1 + z^2)/(1 - z^2)] == -2 ArcCot[z] - Pi /;
Element[(-I) z, Reals] && 0 < (-I) z < 1
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcSec", "[", FractionBox[RowBox[List["1", "+", SuperscriptBox["z", "2"]]], RowBox[List["1", "-", SuperscriptBox["z", "2"]]]], "]"]], "\[Equal]", RowBox[List[RowBox[List[RowBox[List["-", "2"]], RowBox[List["ArcCot", "[", "z", "]"]]]], "-", "\[Pi]"]]]], "/;", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "z"]], "\[Element]", "Reals"]], "\[And]", RowBox[List["0", "<", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "z"]], "<", "1"]]]], ")"]]]]]]
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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> sec </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mfrac> <mrow> <mn> 1 </mn> <mo> + </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mrow> <mn> 1 </mn> <mo> - </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </mfrac> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ⁢ </mo> <mrow> <msup> <mi> cot </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mi> π </mi> </mrow> </mrow> <mo> /; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mrow> <mo> - </mo> <mi> ⅈ </mi> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ∈ </mo> <mi> ℝ </mi> </mrow> <mo> ∧ </mo> <mrow> <mn> 0 </mn> <mo> < </mo> <mrow> <mrow> <mo> - </mo> <mi> ⅈ </mi> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> < </mo> <mn> 1 </mn> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <arcsec /> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <apply> <arccot /> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <pi /> </apply> </apply> </apply> <apply> <and /> <apply> <in /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <ci> z </ci> </apply> <ci> ℝ </ci> </apply> <apply> <lt /> <cn type='integer'> 0 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <ci> z </ci> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcSec", "[", FractionBox[RowBox[List["1", "+", SuperscriptBox["z_", "2"]]], RowBox[List["1", "-", SuperscriptBox["z_", "2"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["ArcCot", "[", "z", "]"]]]], "-", "\[Pi]"]], "/;", RowBox[List[RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "z"]], "\[Element]", "Reals"]], "&&", RowBox[List["0", "<", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "z"]], "<", "1"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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