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http://functions.wolfram.com/01.04.27.0044.01
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Log[z] == ArcCoth[(z^2 + 1)/(z^2 - 1)] /; Re[z] > 0 || I z > 1 || -1 < I z < 0
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Log", "[", "z", "]"]], "\[Equal]", RowBox[List["ArcCoth", "[", FractionBox[RowBox[List[SuperscriptBox["z", "2"], "+", "1"]], RowBox[List[SuperscriptBox["z", "2"], "-", "1"]]], "]"]]]], "/;", RowBox[List[RowBox[List[RowBox[List["Re", "[", "z", "]"]], ">", "0"]], "\[Or]", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "z"]], ">", "1"]], "\[Or]", RowBox[List[RowBox[List["-", "1"]], "<", RowBox[List["\[ImaginaryI]", " ", "z"]], "<", "0"]]]]]]]]
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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> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <msup> <mi> coth </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mfrac> <mrow> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> + </mo> <mn> 1 </mn> </mrow> <mrow> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mn> 1 </mn> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mrow> <mi> Re </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> > </mo> <mn> 0 </mn> </mrow> <mo> ∨ </mo> <mrow> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> > </mo> <mn> 1 </mn> </mrow> <mo> ∨ </mo> <mrow> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> < </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> < </mo> <mn> 0 </mn> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ln /> <ci> z </ci> </apply> <apply> <arccoth /> <apply> <times /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <or /> <apply> <gt /> <apply> <real /> <ci> z </ci> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <gt /> <apply> <times /> <imaginaryi /> <ci> z </ci> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <lt /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> z </ci> </apply> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Log", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["ArcCoth", "[", FractionBox[RowBox[List[SuperscriptBox["z", "2"], "+", "1"]], RowBox[List[SuperscriptBox["z", "2"], "-", "1"]]], "]"]], "/;", RowBox[List[RowBox[List[RowBox[List["Re", "[", "z", "]"]], ">", "0"]], "||", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "z"]], ">", "1"]], "||", RowBox[List[RowBox[List["-", "1"]], "<", RowBox[List["\[ImaginaryI]", " ", "z"]], "<", "0"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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