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variants of this functions
ArcTan




Mathematica Notation

Traditional Notation









Elementary Functions > ArcTan[z] > Transformations > Products, sums, and powers of the direct function > Sums of the direct function





http://functions.wolfram.com/01.14.16.0012.01









  


  








Input Form





ArcTan[x] + ArcTan[y] + ArcTan[z] == 0 /; x + y + z == x y z








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[RowBox[List["ArcTan", "[", "x", "]"]], "+", RowBox[List["ArcTan", "[", "y", "]"]], "+", RowBox[List["ArcTan", "[", "z", "]"]]]], "\[Equal]", "0"]], "/;", RowBox[List[RowBox[List["x", "+", "y", "+", "z"]], "\[Equal]", RowBox[List["x", " ", "y", " ", "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> <mrow> <mrow> <msup> <mi> tan </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <msup> <mi> tan </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> y </mi> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <msup> <mi> tan </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> &#10869; </mo> <mn> 0 </mn> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> x </mi> <mo> + </mo> <mi> y </mi> <mo> + </mo> <mi> z </mi> </mrow> <mo> &#10869; </mo> <mrow> <mi> x </mi> <mo> &#8290; </mo> <mi> y </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <plus /> <apply> <arctan /> <ci> x </ci> </apply> <apply> <arctan /> <ci> y </ci> </apply> <apply> <arctan /> <ci> z </ci> </apply> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <eq /> <apply> <plus /> <ci> x </ci> <ci> y </ci> <ci> z </ci> </apply> <apply> <times /> <ci> x </ci> <ci> y </ci> <ci> z </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["ArcTan", "[", "x_", "]"]], "+", RowBox[List["ArcTan", "[", "y_", "]"]], "+", RowBox[List["ArcTan", "[", "z_", "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List["0", "/;", RowBox[List[RowBox[List["x", "+", "y", "+", "z"]], "\[Equal]", RowBox[List["x", " ", "y", " ", "z"]]]]]]]]]]


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





2001-10-29