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variants of this functions
Log




Mathematica Notation

Traditional Notation









Elementary Functions > Log[z] > Transformations > Transformations and argument simplifications > Argument involving basic arithmetic operations





http://functions.wolfram.com/01.04.16.0055.01









  


  








Input Form





Log[I z] == (I Pi)/2 + 2 I Pi Floor[1/4 - Arg[z]/(2 Pi)] + Log[z]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Log", "[", RowBox[List["\[ImaginaryI]", " ", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]"]], "2"], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "\[Pi]", " ", RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "4"], "-", FractionBox[RowBox[List["Arg", "[", "z", "]"]], RowBox[List["2", " ", "\[Pi]"]]]]], "]"]]]], "+", RowBox[List["Log", "[", "z", "]"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mn> 2 </mn> </mfrac> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> &#960; </mi> <mo> &#8290; </mo> <mrow> <mo> &#8970; </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mi> arg </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> </mfrac> </mrow> <mo> &#8971; </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ln /> <apply> <times /> <imaginaryi /> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <imaginaryi /> <pi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <pi /> <apply> <floor /> <apply> <plus /> <cn type='rational'> 1 <sep /> 4 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <arg /> <ci> z </ci> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <ln /> <ci> z </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Log", "[", RowBox[List["\[ImaginaryI]", " ", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]"]], "2"], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "\[Pi]", " ", RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "4"], "-", FractionBox[RowBox[List["Arg", "[", "z", "]"]], RowBox[List["2", " ", "\[Pi]"]]]]], "]"]]]], "+", RowBox[List["Log", "[", "z", "]"]]]]]]]]


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





2007-05-02