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variants of this functions
Log




Mathematica Notation

Traditional Notation









Elementary Functions > Log[z] > Representations through equivalent functions > With related functions > Involving sec-1





http://functions.wolfram.com/01.04.27.0022.01









  


  








Input Form





Log[z] == I ArcSec[(2 z)/(1 + z^2)] /; Im[z] > 0 || z <= -1 || Inequality[0, Less, z, LessEqual, 1]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Log", "[", "z", "]"]], "\[Equal]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSec", "[", FractionBox[RowBox[List["2", "z"]], RowBox[List["1", "+", SuperscriptBox["z", "2"]]]], "]"]]]]]], "/;", RowBox[List[RowBox[List[RowBox[List["Im", "[", "z", "]"]], ">", "0"]], "\[Or]", RowBox[List["z", "\[LessEqual]", RowBox[List["-", "1"]]]], "\[Or]", RowBox[List["0", "<", "z", "\[LessEqual]", "1"]]]]]]]]








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> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <msup> <mi> sec </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mrow> <mn> 1 </mn> <mo> + </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mrow> <mi> Im </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &gt; </mo> <mn> 0 </mn> </mrow> <mo> &#8744; </mo> <mrow> <mi> z </mi> <mo> &#8804; </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </mrow> <mo> &#8744; </mo> <mrow> <mn> 0 </mn> <mo> &lt; </mo> <mi> z </mi> <mo> &#8804; </mo> <mn> 1 </mn> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ln /> <ci> z </ci> </apply> <apply> <times /> <imaginaryi /> <apply> <arcsec /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <or /> <apply> <gt /> <apply> <imaginary /> <ci> z </ci> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <leq /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <apply> <ci> Inequality </ci> <cn type='integer'> 0 </cn> <lt /> <ci> z </ci> <leq /> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Log", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSec", "[", FractionBox[RowBox[List["2", " ", "z"]], RowBox[List["1", "+", SuperscriptBox["z", "2"]]]], "]"]]]], "/;", RowBox[List[RowBox[List[RowBox[List["Im", "[", "z", "]"]], ">", "0"]], "||", RowBox[List["z", "\[LessEqual]", RowBox[List["-", "1"]]]], "||", RowBox[List["0", "<", "z", "\[LessEqual]", "1"]]]]]]]]]]


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





2001-10-29