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variants of this functions
ArcTan




Mathematica Notation

Traditional Notation









Elementary Functions > ArcTan[z] > Representations through equivalent functions > With related functions > Involving cot-1 > Involving tan-1(1+z/1-z) > Involving tan-1(1+z/1-z) and cot-1(z)





http://functions.wolfram.com/01.14.27.0675.01









  


  








Input Form





ArcTan[(1 + z)/(1 - z)] == -ArcCot[z] - Pi/4 /; Abs[z] > 1 || Re[z] < 0








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcTan", "[", FractionBox[RowBox[List["1", "+", "z"]], RowBox[List["1", "-", "z"]]], "]"]], "\[Equal]", RowBox[List[RowBox[List["-", RowBox[List["ArcCot", "[", "z", "]"]]]], "-", FractionBox["\[Pi]", "4"]]]]], "/;", RowBox[List[RowBox[List[RowBox[List["Abs", "[", "z", "]"]], ">", "1"]], "\[Or]", RowBox[List[RowBox[List["Re", "[", "z", "]"]], "<", "0"]]]]]]]]








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> <msup> <mi> tan </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mfrac> <mrow> <mn> 1 </mn> <mo> + </mo> <mi> z </mi> </mrow> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> </mfrac> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <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> <mfrac> <mi> &#960; </mi> <mn> 4 </mn> </mfrac> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[LeftBracketingBar]&quot; </annotation> </semantics> <mi> z </mi> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[RightBracketingBar]&quot; </annotation> </semantics> </mrow> <mo> &gt; </mo> <mn> 1 </mn> </mrow> <mo> &#8744; </mo> <mrow> <mrow> <mi> Re </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &lt; </mo> <mn> 0 </mn> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <arctan /> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <ci> z </ci> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <arccot /> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <or /> <apply> <gt /> <apply> <abs /> <ci> z </ci> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <lt /> <apply> <real /> <ci> z </ci> </apply> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcTan", "[", FractionBox[RowBox[List["1", "+", "z_"]], RowBox[List["1", "-", "z_"]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["-", RowBox[List["ArcCot", "[", "z", "]"]]]], "-", FractionBox["\[Pi]", "4"]]], "/;", RowBox[List[RowBox[List[RowBox[List["Abs", "[", "z", "]"]], ">", "1"]], "||", RowBox[List[RowBox[List["Re", "[", "z", "]"]], "<", "0"]]]]]]]]]]


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





2003-08-21